https://wildtopology.com/about/2026-03-13T04:07:25+00:00weekly0.6https://wildtopology.com/problemlist/https://wildtopology.com/wp-content/uploads/2019/09/ptau-2.pngptau2026-02-21T16:36:25+00:00weekly0.6https://wildtopology.com/2019/08/06/shape-injectivity-of-the-hawaiian-earring-part-ii/https://wildtopology.com/wp-content/uploads/2019/08/up3.pngup3https://wildtopology.com/wp-content/uploads/2019/08/up2.pngup2https://wildtopology.com/wp-content/uploads/2019/08/up1.pngup1https://wildtopology.com/wp-content/uploads/2019/08/ilim5.pngilim5https://wildtopology.com/wp-content/uploads/2019/08/ilim4.pngilim4https://wildtopology.com/wp-content/uploads/2019/08/contr3-1.pngcontr3https://wildtopology.com/wp-content/uploads/2019/08/contr2.pngcontr2https://wildtopology.com/wp-content/uploads/2019/08/contr.pngcontr2026-01-18T16:11:27+00:00monthlyhttps://wildtopology.com/bestiary/sierpinski-carpet/https://wildtopology.com/wp-content/uploads/2025/06/sierpinski-carpet.pngSierpinski CarpetThe Sierpinski Carpet2025-11-07T22:37:21+00:00weekly0.6https://wildtopology.com/2025/11/05/inverse-limits-of-planar-peano-continua-are-not-always-planar/https://wildtopology.com/wp-content/uploads/2025/11/l2.pngl2https://wildtopology.com/wp-content/uploads/2025/11/invsystem.pnginvsystemhttps://wildtopology.com/wp-content/uploads/2025/11/l1approx2.pngL1approx2https://wildtopology.com/wp-content/uploads/2025/11/l1approx.pngL1approxhttps://wildtopology.com/wp-content/uploads/2025/11/l1.pngL1https://wildtopology.com/wp-content/uploads/2025/11/k33k5.pngk33k52025-11-05T21:36:40+00:00monthlyhttps://wildtopology.com/bestiary/the-alternating-cone-space/https://wildtopology.com/wp-content/uploads/2025/06/asc3.pngasc32025-06-29T15:05:03+00:00weekly0.6https://wildtopology.com/bestiary/warsaw-circle/https://wildtopology.com/wp-content/uploads/2020/04/warsaw.pngwarsaw2025-06-22T14:47:19+00:00weekly0.6https://wildtopology.com/bestiary/the-n-dimensional-earring/https://wildtopology.com/wp-content/uploads/2022/01/convsequence.pngconvsequence$latex \mathbb{E}_0$ is a convergent sequence. The basepoint, is the limit point illustrated as the larger blue point.https://wildtopology.com/wp-content/uploads/2022/01/2d-hawaiian-earring-02.png2d Hawaiian Earring 02The 2-dimensional earringhttps://wildtopology.com/wp-content/uploads/2022/01/he.pnghe2025-06-22T14:45:51+00:00weekly0.6https://wildtopology.com/bestiary/shrinking-wedge-of-tori/https://wildtopology.com/wp-content/uploads/2020/05/shrinkingtorus2.jpgshrinkingtorus2The Hawaiian earring as a subspace of the shrinking wedge of tori.https://wildtopology.com/wp-content/uploads/2020/05/shrinkingtorus.jpgshrinkingtorusShrinking wedge of tori2025-06-22T14:42:56+00:00weekly0.6https://wildtopology.com/bestiary/hawaiian-pants/https://wildtopology.com/wp-content/uploads/2020/06/hawaiianpants.pnghawaiianpantsConstruction of the Hawaiian pants2025-06-22T14:42:29+00:00weekly0.6https://wildtopology.com/bestiary/the-wild-circle/https://wildtopology.com/wp-content/uploads/2020/06/wildcircle.pngwildcircleThe wild circle2025-06-22T14:42:09+00:00weekly0.6https://wildtopology.com/bestiary/edwards-continuum/2025-06-22T14:41:51+00:00weekly0.6https://wildtopology.com/bestiary/double-earring/https://wildtopology.com/wp-content/uploads/2020/04/dhe.pngdhe2025-06-22T14:41:21+00:00weekly0.6https://wildtopology.com/bestiary/cantor-fan/2025-06-22T14:39:47+00:00weekly0.6https://wildtopology.com/bestiary/https://wildtopology.com/wp-content/uploads/2019/12/perindens.jpgPerindens2025-06-22T14:20:54+00:00weekly0.6https://wildtopology.com/2022/06/30/topologized-fundamental-groups-the-whisker-topology-part-3/https://wildtopology.com/wp-content/uploads/2022/06/arcspace2.pngarcspace2Attaching a shrinking sequence of 2-spheres to the earring space as illustrated gives $latex \mathbb{E}_1\vee\mathbb{E}_2$.https://wildtopology.com/wp-content/uploads/2022/06/arcspace.pngarcspaceA sequence of shrinking 2-spheres attached to an arc.2025-01-31T20:54:52+00:00monthlyhttps://wildtopology.com/2024/09/19/topological-group-reflections-turning-a-group-with-topology-into-a-topological-group-part-i/2024-11-17T05:15:27+00:00monthlyhttps://wildtopology.com/2022/05/24/topologized-fundamental-groups-the-whisker-topology-part-2/https://wildtopology.com/wp-content/uploads/2022/05/griffithscircle.pnggriffithscircleThe Griffiths twin cone with an extra circle attached.https://wildtopology.com/wp-content/uploads/2022/05/whisker4.pngwhisker4Proof of the Neighborhood Lemma in $latex \widetilde{X}$.https://wildtopology.com/wp-content/uploads/2022/05/whisker3.pngwhisker3The whisker topology becomes a group topology if and only if for every $latex \beta$ and neighborhood $latex U$, there exists a neighborhood $latex V$ such that for any loop $latex \epsilon$ in $latex V$, the conjugate $latex \beta\cdot\epsilon\cdot\beta^{-}$ is homotopic to some loop in $latex U$.https://wildtopology.com/wp-content/uploads/2022/05/whisker1.pngwhisker1A basic neighborhood of an element $latex [\alpha]$ in the fundamental group consists of homotopy classes of the form $latex [\alpha\cdot\epsilon]$.https://wildtopology.com/wp-content/uploads/2022/05/whisker2.pngwhisker2Visualizing a basic neighborhood of $latex [\alpha]$ in the whisker topology2024-11-12T22:59:15+00:00monthlyhttps://wildtopology.com/2022/05/18/topologized-fundamental-groups-the-whisker-topology-part-1/2024-11-12T22:58:23+00:00monthlyhttps://wildtopology.com/2022/04/26/how-to-topologize-the-fundamental-group-a-primer/https://wildtopology.com/wp-content/uploads/2021/01/im5.pngim5https://wildtopology.com/wp-content/uploads/2021/01/im4.pngim4https://wildtopology.com/wp-content/uploads/2021/01/im3.pngim3https://wildtopology.com/wp-content/uploads/2021/01/im2.pngim2https://wildtopology.com/wp-content/uploads/2021/01/im1.pngim12024-11-09T01:51:47+00:00monthlyhttps://wildtopology.com/2024/11/09/the-tau-topology-on-the-fundamental-group/2024-11-09T01:50:52+00:00monthlyhttps://wildtopology.com/2023/04/18/__trashed/https://wildtopology.com/wp-content/uploads/2023/04/fan2-1.pngfan2-1https://wildtopology.com/wp-content/uploads/2023/04/fufan.pngfufanhttps://wildtopology.com/wp-content/uploads/2023/04/fan2.pngfan22024-11-09T00:06:51+00:00monthlyhttps://wildtopology.com/2023/10/07/topologized-fundamental-groups-the-quotient-topology-part-4-subgroup-classifications/2024-11-09T00:03:13+00:00monthlyhttps://wildtopology.com/2023/02/13/topologized-fundamental-groups-the-quotient-topology-part-2-discreteness/https://wildtopology.com/wp-content/uploads/2023/02/discrete4.pngdiscrete4The path $latex \beta$ and the connecting paths $latex \gamma_j$.https://wildtopology.com/wp-content/uploads/2023/02/discrete3.pngdiscrete3A close-up view of the general case where we have create a loop in $latex U_j$ with corresponding portions of $latex \alpha$ and $latex \beta$.https://wildtopology.com/wp-content/uploads/2023/02/discrete2.pngdiscrete2The neighborhood $latex \mathscr{U}$ of $latex \alpha$.https://wildtopology.com/wp-content/uploads/2023/02/discrete1.pngdiscrete12024-11-09T00:01:12+00:00monthlyhttps://wildtopology.com/2022/08/25/topologized-fundamental-groups-the-quotient-topology-part-1/https://wildtopology.com/wp-content/uploads/2022/08/qtop6-1.pngqtop6https://wildtopology.com/wp-content/uploads/2022/08/qtop5.pngqtop5https://wildtopology.com/wp-content/uploads/2022/08/qtop4.pngqtop4https://wildtopology.com/wp-content/uploads/2022/08/qtop3.pngqtop3https://wildtopology.com/wp-content/uploads/2022/08/qtop2.pngqtop2https://wildtopology.com/wp-content/uploads/2022/08/qtop1.pngqtop1https://wildtopology.com/wp-content/uploads/2022/08/cotopology.pngcotopologyA basic open set in the compact open topology2024-11-09T00:00:15+00:00monthlyhttps://wildtopology.com/2024/11/06/topological-group-reflections-turning-a-group-with-topology-into-a-topological-group-part-ii/https://wildtopology.com/wp-content/uploads/2024/11/diag1.pngdiag12024-11-06T03:13:27+00:00monthlyhttps://wildtopology.com/2023/10/08/local-n-connectivity-vs-the-lcn-property/https://wildtopology.com/wp-content/uploads/2023/10/lcn5.pnglcn5https://wildtopology.com/wp-content/uploads/2023/10/lcn4.pnglcn4https://wildtopology.com/wp-content/uploads/2023/10/lcn1-1.pnglcn1-1https://wildtopology.com/wp-content/uploads/2023/10/lcn1.pnglcn12024-07-03T17:14:58+00:00monthlyhttps://wildtopology.com/2023/10/17/local-n-connectivity-vs-the-lcn-property-part-2/https://wildtopology.com/wp-content/uploads/2023/10/shrinkingcones.pngshrinkingconeshttps://wildtopology.com/wp-content/uploads/2023/10/gillespiesspace.pnggillespiesspace2023-10-18T11:45:25+00:00monthlyhttps://wildtopology.com/bestiary/hawaiian-earring/https://wildtopology.com/wp-content/uploads/2019/12/he.pnghe2022-09-20T03:17:18+00:00weekly0.6https://wildtopology.com/2014/12/06/the-locally-path-connected-coreflection-iii/https://wildtopology.com/wp-content/uploads/2014/12/coreflectionproof.pngcoreflectionproofConstructing $latex f:ah(J)\to X$https://wildtopology.com/wp-content/uploads/2014/12/archedgehog.pngarchedgehogOmega arc-hedgehog2022-08-03T15:26:16+00:00monthlyhttps://wildtopology.com/2014/10/11/the-locally-path-connected-coreflection/https://wildtopology.com/wp-content/uploads/2014/10/genwedge3.pngpath components of a neighborhoodhttps://wildtopology.com/wp-content/uploads/2014/10/genwedge2.pngthe lpc-coreflection of a generalized wedge of circleshttps://wildtopology.com/wp-content/uploads/2014/10/genwedge1.pnggeneralized wedge of circles2022-04-10T03:28:29+00:00monthlyhttps://wildtopology.com/2022/01/01/when-is-a-local-homeomorphism-a-semicovering-map/https://wildtopology.com/wp-content/uploads/2022/01/sineproj.pngsineproj2022-01-01T19:30:41+00:00monthlyhttps://wildtopology.com/bestiary/blue-sky-catastrophe/https://wildtopology.com/wp-content/uploads/2021/12/the-hormos-e28094-topological-semigroup.pngthe hormos — topological semigroupThe universal connected cover of $latex B$ (the two limiting points in the picture are not included). Image from: "The structure of topological semigroups — revisited", Paul S. Mostert. Bull. AMS 1966.https://wildtopology.com/wp-content/uploads/2021/12/asymptotic-ouroboros.pngAsymptotic Ouroboros2021-12-31T20:07:58+00:00weekly0.6https://wildtopology.com/2012/10/30/the-cech-expansion-i-nerves-of-open-covers/https://wildtopology.com/wp-content/uploads/2012/10/hoop.pnghoopThe space $latex Y$: a wedge of converging circleshttps://wildtopology.com/wp-content/uploads/2012/10/1skel.png1-skeleton1-skeletonhttps://wildtopology.com/wp-content/uploads/2012/10/0skel.png0-skeleton0-skeletonhttps://wildtopology.com/wp-content/uploads/2012/10/example1.pngcover$latex\mathscr{U}$https://wildtopology.com/wp-content/uploads/2012/10/tetrahedron.pngtetrahedrontetrahedronhttps://wildtopology.com/wp-content/uploads/2012/10/circlecover3.pngCircle cover 3https://wildtopology.com/wp-content/uploads/2012/10/circlecover22.pngcirclecover2https://wildtopology.com/wp-content/uploads/2012/10/circlecover21.pngCircle coverhttps://wildtopology.com/wp-content/uploads/2012/10/circlecover1.pngCircle cover 2https://wildtopology.com/wp-content/uploads/2012/10/circlecover2.pngcirclecover22021-12-30T15:59:14+00:00monthlyhttps://wildtopology.com/2014/05/18/the-harmonic-archipelago-group-is-not-free/2021-12-30T15:56:55+00:00monthlyhttps://wildtopology.com/2014/06/07/homomorphisms-from-the-hawaiian-earring-group-to-finite-groups/https://wildtopology.com/wp-content/uploads/2014/06/finitegroup1.pngfinitegroup12021-12-30T15:55:20+00:00monthlyhttps://wildtopology.com/2017/03/18/homotopically-hausdorff-spaces-ii/https://wildtopology.com/wp-content/uploads/2017/03/homotopy3.pngVerifying continuityhttps://wildtopology.com/wp-content/uploads/2017/03/homotopy21.pngInfinite concatenation of null-homotopieshttps://wildtopology.com/wp-content/uploads/2017/03/homotopy11.pngSingle null-homotopyhttps://wildtopology.com/wp-content/uploads/2017/03/infprod.pngInfinite ConcatenationInfinite Concatenationhttps://wildtopology.com/wp-content/uploads/2017/03/he.pngHawaiian earring space2021-12-30T15:53:25+00:00monthlyhttps://wildtopology.com/2019/07/31/shape-injectivity-of-the-hawaiian-earring-part-i/https://wildtopology.com/wp-content/uploads/2019/07/up4.pngup4https://wildtopology.com/wp-content/uploads/2019/07/ilim2-3-1-e1564615661322.pngilim2https://wildtopology.com/wp-content/uploads/2019/07/ilim3.pngilim3https://wildtopology.com/wp-content/uploads/2019/07/ilim2-2.pngilim2https://wildtopology.com/wp-content/uploads/2019/07/is5.pngis5https://wildtopology.com/wp-content/uploads/2019/07/is1.pngis1https://wildtopology.com/wp-content/uploads/2019/07/ilim.pngilimhttps://wildtopology.com/wp-content/uploads/2019/07/is8.pngis8https://wildtopology.com/wp-content/uploads/2019/07/is7.pngis7https://wildtopology.com/wp-content/uploads/2019/03/is6.pngis62021-12-30T15:48:28+00:00monthlyhttps://wildtopology.com/2014/05/09/the-hawaiian-earring-group-is-not-free-part-i/https://wildtopology.com/wp-content/uploads/2014/05/selfhomomorphism.pngselfhomomorphism2021-12-30T15:42:21+00:00monthlyhttps://wildtopology.com/2013/11/23/the-hawaiian-earring/https://wildtopology.com/wp-content/uploads/2013/11/helimit.pnghelimithttps://wildtopology.com/wp-content/uploads/2013/11/he.pnghe2024-06-27T22:59:08+00:00monthlyhttps://wildtopology.com/2014/05/16/the-hawaiian-earring-group-is-not-free-part-ii/2021-12-30T15:40:03+00:00monthlyhttps://wildtopology.com/2020/10/18/testing-the-limits-of-edas-theorem/https://wildtopology.com/wp-content/uploads/2020/10/spacey.pngspaceyThe Space $latex Y$https://wildtopology.com/wp-content/uploads/2020/10/induced-1.pnginduced2021-12-30T15:36:58+00:00monthlyhttps://wildtopology.com/2012/05/08/a-starting-place/2021-12-30T15:34:49+00:00monthlyhttps://wildtopology.com/2021/08/21/visualizing-the-hopf-fibration/2021-09-01T15:06:20+00:00monthlyhttps://wildtopology.com/2014/07/02/the-baer-specker-group/https://wildtopology.com/wp-content/uploads/2014/07/speckerpost.pngspeckerposthttps://wildtopology.com/wp-content/uploads/2014/07/speckertriangle1.pnghttps://wildtopology.com/wp-content/uploads/2014/07/speckertriangle.pngspeckertriangle2022-07-04T00:27:20+00:00monthlyhttps://wildtopology.com/2014/06/28/the-griffiths-twin-cone/https://wildtopology.com/wp-content/uploads/2014/06/griffiths31.pngOpen cover of the Griffiths twin conehttps://wildtopology.com/wp-content/uploads/2014/06/griffiths3.pngCover of the Griffiths twin conehttps://wildtopology.com/wp-content/uploads/2014/06/griffiths2.pnggriffiths2Alternative construction of the Griffiths twin conehttps://wildtopology.com/wp-content/uploads/2014/06/griffiths1.pnggriffiths1Griffiths twin cone2021-08-29T15:50:16+00:00monthlyhttps://wildtopology.com/bestiary/griffiths-twin-cone/2021-08-29T15:43:15+00:00weekly0.6https://wildtopology.com/2014/05/01/the-harmonic-archipelago/https://wildtopology.com/wp-content/uploads/2014/05/hapost2.pnghapost2https://wildtopology.com/wp-content/uploads/2014/05/hapost1.pnghapost1https://wildtopology.com/wp-content/uploads/2014/05/haholes2-1.pnghaholes2https://wildtopology.com/wp-content/uploads/2014/05/haholes-1.pnghaholeshttps://wildtopology.com/wp-content/uploads/2014/05/hachopped.pngHAchoppedMostly chopped Harmonic Archipelagohttps://wildtopology.com/wp-content/uploads/2014/05/ha.pngHAThe Harmonic Archipelago Spacehttps://wildtopology.com/wp-content/uploads/2014/05/dirsys2.pngdirsys2https://wildtopology.com/wp-content/uploads/2014/05/dirsys.pngdirected systemhttps://wildtopology.com/wp-content/uploads/2014/05/haholes.pnghaholeshttps://wildtopology.com/wp-content/uploads/2014/05/haholes2.pnghaholes22021-08-29T15:13:02+00:00monthlyhttps://wildtopology.com/2018/05/16/celebrating-the-career-and-contributions-of-katsuya-eda-master-of-the-hawaiian-earring/https://wildtopology.com/wp-content/uploads/2018/05/katsuyaeda2.jpgkatsuyaeda2https://wildtopology.com/wp-content/uploads/2018/05/katsuyaeda1.jpgkatsuyaeda1Katsuya Eda at the Arches Topology Conferencehttps://wildtopology.com/wp-content/uploads/2018/05/img_20180510_123550.jpgIMG_20180510_1235502021-08-26T18:54:43+00:00monthlyhttps://wildtopology.com/bestiary/hawaiian-mapping-torus/https://wildtopology.com/wp-content/uploads/2019/12/hmt3.pnghmt3https://wildtopology.com/wp-content/uploads/2019/12/hmt2.jpghmt2https://wildtopology.com/wp-content/uploads/2019/12/hawaiianspiral.jpghawaiianspiral2021-08-25T03:10:36+00:00weekly0.6https://wildtopology.com/2021/07/19/what-is-a-semicovering-map/https://wildtopology.com/wp-content/uploads/2021/07/semicovering.pngA semicovering over the earring spaceA non-trivial semicovering over the earring space, which is not a covering map. Each step that moves you one edge away from the given basepoint, unwraps the next circle of the earring.https://wildtopology.com/wp-content/uploads/2021/06/endpoint3-1.pngendpoint3https://wildtopology.com/wp-content/uploads/2021/06/endpoint2.pngendpoint2https://wildtopology.com/wp-content/uploads/2021/06/endpoint.pngendpointhttps://wildtopology.com/wp-content/uploads/2021/06/basis.jpgbasishttps://wildtopology.com/wp-content/uploads/2021/06/xl3ki.pngXL3kiA composition of two covering maps, which is a semicovering map but not a covering map.2021-07-20T16:20:34+00:00monthlyhttps://wildtopology.com/2019/11/23/higher-dimensional-hawaiian-earrings/https://wildtopology.com/wp-content/uploads/2019/11/up7.pngup7https://wildtopology.com/wp-content/uploads/2019/11/up6.pngup6https://wildtopology.com/wp-content/uploads/2019/11/up5.pngup5https://wildtopology.com/wp-content/uploads/2019/11/ses3.pngses3https://wildtopology.com/wp-content/uploads/2019/11/les4.pngles4https://wildtopology.com/wp-content/uploads/2019/11/les3.pngles3https://wildtopology.com/wp-content/uploads/2019/11/ses2.pngses2https://wildtopology.com/wp-content/uploads/2019/11/les2.pngles2https://wildtopology.com/wp-content/uploads/2019/11/les1.pngles1https://wildtopology.com/wp-content/uploads/2019/11/higherinfproduct.pnghigherinfproduct2021-07-19T18:47:48+00:00monthlyhttps://wildtopology.com/2021/07/12/the-griffiths-twin-cone-and-the-harmonic-archipelago-have-isomorphic-fundamental-group-part-3/2021-07-12T08:39:00+00:00monthlyhttps://wildtopology.com/bestiary/harmonic-archipelago/2021-06-21T20:18:15+00:00weekly0.6https://wildtopology.com/bestiary/dyadic-arc-space/https://wildtopology.com/wp-content/uploads/2019/12/trianglecontinuum.pngtrianglecontinuumhttps://wildtopology.com/wp-content/uploads/2019/12/dyadircarcspace.pngdyadircarcspace2021-06-21T19:52:51+00:00weekly0.6https://wildtopology.com/2020/08/03/infinite-commutativity-part-ii/https://wildtopology.com/wp-content/uploads/2020/08/ndomain2.pngndomain2https://wildtopology.com/wp-content/uploads/2020/08/ndomain5.pngndomain5https://wildtopology.com/wp-content/uploads/2020/08/ndomain1.pngndomain1Some examples of n-domainshttps://wildtopology.com/wp-content/uploads/2020/08/inf2prod.pnginf2prodInfinite product of 2-loopshttps://wildtopology.com/wp-content/uploads/2020/08/eh3.pngeh3https://wildtopology.com/wp-content/uploads/2020/08/eh2.pngeh2https://wildtopology.com/wp-content/uploads/2020/08/eh1.pngeh1https://wildtopology.com/wp-content/uploads/2020/08/shuffle0.pngshuffle0Infinite concatenation of 2-loops.2021-06-20T17:22:53+00:00monthlyhttps://wildtopology.com/2021/06/07/the-griffiths-twin-cone-and-the-harmonic-archipelago-have-isomorphic-fundamental-group-part-1/https://wildtopology.com/wp-content/uploads/2021/06/haandgtc.pngHAandGTCGriffiths twin cone (left) and the harmonic archipelago (right).2021-06-20T17:18:14+00:00monthlyhttps://wildtopology.com/2021/06/14/the-griffiths-twin-cone-and-the-harmonic-archipelago-have-isomorphic-fundamental-group-part-2/2021-06-20T17:15:07+00:00monthlyhttps://wildtopology.com/2020/12/26/homotopically-reduced-paths-part-iii/https://wildtopology.com/wp-content/uploads/2020/12/reduced2.pngreduced2The homotopy $latex H$ is the constant homotopy on $latex A\times [0,1]$ (shaded in blue). For components $latex J$ of $latex [0,1]\backslash A$, $latex H$ is defined as $latex H_J$ on $latex \overline{J}\times [0,1]$ (the white boxes).https://wildtopology.com/wp-content/uploads/2020/12/reduced1.pngreduced1In one-dimensional spaces, a concatenation of two reduced paths can only reduce by a cancelation of a terminal subpath of the first path and an initial subpath of the second path. The terminal subpath must be a reparameterization of the reverse of the initial subpath.https://wildtopology.com/wp-content/uploads/2020/12/tree3-1.pngtree3https://wildtopology.com/wp-content/uploads/2020/12/tree3.pngtree3https://wildtopology.com/wp-content/uploads/2020/12/trees2.pngtrees2https://wildtopology.com/wp-content/uploads/2020/12/trees1.pngtrees12021-06-20T17:13:55+00:00monthlyhttps://wildtopology.com/2020/12/23/homotopically-reduced-paths-part-ii/https://wildtopology.com/wp-content/uploads/2020/12/blog3.pngblog3https://wildtopology.com/wp-content/uploads/2020/12/blog2-1.pngblog2https://wildtopology.com/wp-content/uploads/2020/12/blog2.pngblog2https://wildtopology.com/wp-content/uploads/2020/12/welldefined1.pngwelldefined12021-06-09T12:06:52+00:00monthlyhttps://wildtopology.com/2020/12/18/homotopically-reduced-paths-part-i/https://wildtopology.com/wp-content/uploads/2020/12/blog1-1.pngblog1Altering a path to be constant on a given (possibly infinite) family of subloops.https://wildtopology.com/wp-content/uploads/2020/12/blog1.pngblog1Altering a path to be constant on a given (possibly infinite) family of subloops.https://wildtopology.com/wp-content/uploads/2020/12/cantormap.pngcantormapThe Cantor Functionhttps://wildtopology.com/wp-content/uploads/2020/12/cylinderhomotopy.gifcylinderhomotopyA family of reduced loops all representing the same homotopy class.2021-04-05T16:53:52+00:00monthlyhttps://wildtopology.com/2020/08/02/infinite-commutativity-part-i/https://wildtopology.com/wp-content/uploads/2020/08/eckmannhilton2a.gifeckmannhilton2ahttps://wildtopology.com/wp-content/uploads/2020/08/eckmann.gifeckmann_brazasEckmann Hilton Homotopyhttps://wildtopology.com/wp-content/uploads/2019/09/eckmannhilton.gifeckmannhiltonhttps://wildtopology.com/wp-content/uploads/2019/08/2dim.png2dim2020-12-23T00:16:49+00:00monthlyhttps://wildtopology.com/2019/12/15/spanier-groups-vintage-covering-space-theory/https://wildtopology.com/wp-content/uploads/2019/12/bcs.pngbcshttps://wildtopology.com/wp-content/uploads/2019/12/lassospace.pnglassospacehttps://wildtopology.com/wp-content/uploads/2019/12/spanier.pngspanier2020-06-30T02:52:53+00:00monthlyhttps://wildtopology.com/2019/08/14/topological-wildness-vs-algebraic-wildness/https://wildtopology.com/wp-content/uploads/2019/08/wildness3.pngwildness3https://wildtopology.com/wp-content/uploads/2019/08/wildness2.pngwildness2https://wildtopology.com/wp-content/uploads/2019/08/wildness.pngwildnesshttps://wildtopology.com/wp-content/uploads/2019/08/hoopspace.pnghoopspacehttps://wildtopology.com/wp-content/uploads/2019/08/wildset.pngwildsethttps://wildtopology.com/wp-content/uploads/2019/08/dyadircarcspace.pngdyadircarcspaceThe dyadic arc space2019-11-23T22:13:05+00:00monthlyhttps://wildtopology.com/2014/11/06/the-locally-path-connected-coreflection-ii/https://wildtopology.com/wp-content/uploads/2014/10/ineq21.pngineq2https://wildtopology.com/wp-content/uploads/2014/10/ineq11.pngineq1https://wildtopology.com/wp-content/uploads/2014/10/ineq2.pngineq2https://wildtopology.com/wp-content/uploads/2014/10/ineq1.pngineq12019-09-09T23:07:12+00:00monthlyhttps://wildtopology.com/2017/03/14/homotopically-hausdorff-spaces-i/https://wildtopology.com/wp-content/uploads/2017/03/construction.pngconstructionAn element in $latex B([alpha],U)$https://wildtopology.com/wp-content/uploads/2017/03/construction2.pngconstruction2elements of $latex pi(x,U)$https://wildtopology.com/wp-content/uploads/2017/03/coveringcondition.pngcoveringconditionhttps://wildtopology.com/wp-content/uploads/2017/03/twincone.pngtwinconeGriffiths Twin Conehttps://wildtopology.com/wp-content/uploads/2017/03/ha.pngThe harmonic archipelagoThe harmonic archipelago $latex \mathbb{HA}$. Notice the Hawaiian earring $latex \mathbb{H}$ is a subspace and every loop based at the one wild point $latex b_0$ may be contracted to lie within an arbitrary neighborhood of $latex b_0$.2019-09-09T22:56:21+00:00monthlyhttps://wildtopology.com/2019/09/08/new-problem-list/2019-09-08T16:06:58+00:00monthlyhttps://wildtopology.com/2018/08/13/what-is-an-infinite-word-part-i/2019-08-27T19:44:38+00:00monthlyhttps://wildtopology.com/2014/09/07/ptm-dmv-conference-wild-algebraic-geometric-topology-session/https://wildtopology.com/wp-content/uploads/2014/09/bbd1.pngbbd12014-09-22T14:54:28+00:00monthlyhttps://wildtopology.com/2014/06/08/homomorphisms-from-the-harmonic-archipelago-group-to-finite-groups/https://wildtopology.com/wp-content/uploads/2014/06/finitegroup2.pngfinitegroup22014-06-29T17:52:02+00:00monthlyhttps://wildtopology.com/2014/05/23/the-uncountability-of-harmonic-archipelago-group/https://wildtopology.com/wp-content/uploads/2014/05/sesheha.pngsesheha2014-06-25T16:22:46+00:00monthlyhttps://wildtopology.comdaily1.02026-03-13T04:07:25+00:00