Archives
 August 2022
 June 2022
 May 2022
 April 2022
 January 2022
 August 2021
 July 2021
 June 2021
 December 2020
 October 2020
 August 2020
 December 2019
 November 2019
 September 2019
 August 2019
 July 2019
 August 2018
 May 2018
 March 2017
 December 2014
 November 2014
 October 2014
 September 2014
 July 2014
 June 2014
 May 2014
 November 2013
 October 2012
 May 2012
Categories
 Algebraic Topology
 BaerSpecker group
 Cardinality
 Categorical Topology
 Category Theory
 Cech expansion
 compactopen topology
 Conferences
 coreflection functor
 Covering Space Theory
 Dendrite
 earring group
 earring space
 Finite groups
 Free abelian groups
 Free groups
 Fundamental group
 Fundamental groupoid
 General topology
 Generalized covering space theory
 Griffiths twin cone
 Group homomorphisms
 Group theory
 harmonic archipelago
 Higher Homotopy groups
 homotopically Hausdorff
 Homotopy theory
 Infinite Group Theory
 Infinite products
 Inverse Limit
 locally path connected
 onedimensional spaces
 Order Theory
 Peano continuum
 Quasitopological groups
 quotient topology
 reduced paths
 semicovering
 Shape homotopy group
 Shape theory
 Simplicial complexes
 Singular homology
 topological fundamental group
 Topological groups
 Tree
 Ultrafilter
 Uncategorized
Tweets
 Today we talked about the "monoid" of words in the latin alphabet + space. They were fascinated that this could be… twitter.com/i/web/status/1… 2 weeks ago
 RT @MarissaKawehi: Reminder that we are collecting signatures until we send this letter to the AMS Notices on September 30th! Mathematician… 2 weeks ago
 Why aren't free groups taught as standard examples in many undergrad algebra classes? I feel like in most books i… twitter.com/i/web/status/1… 3 weeks ago

This work is licensed under a Creative Commons Attribution 4.0 International License.
Category Archives: Shape theory
Shape injectivity of the earring space (Part II)
This is the sequel to Shape injectivity of the earring space (Part I) We’re on our way to proving the canonical homomorphism from the earring group to the inverse limit of free groups is injective. Part I was mostly dedicated … Continue reading
Shape injectivity of the earring space (Part I)
One of my posts where I did some substantial handwaving is my original post on the fundamental group of the earring space. I wrote about how to understand and work with this group, but I never gave a proof of … Continue reading
The Cech Expansion: nerves of open covers
The Whitehead theorem in homotopy theory basically says that to fully understand the homotopy type of a CWcomplex one only needs to know about the homotopy groups (really, the weak homotopy type). It is very easy to produce spaces to … Continue reading