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
 RT @HigherGeometer: RIP Bill Lawvere 1937–2023 1 week ago
 RT @angryfermion: imagine carrying a child for 9 months just to have them major in mathematics 1 week ago
 Lol my university trying to tell me that SSET stands for student success & engagement team. 3 weeks ago
 Wow. Nick Cave’s exhibit at the Guggenheim is incredible. The sound suits are stunning in person. 3 weeks ago
 Very on board with this. twitter.com/Singularitaria… 1 month ago

This work is licensed under a Creative Commons Attribution 4.0 International License.
Tag Archives: uncountable
Homomorphisms from the harmonic archipelago group to finite groups
This post is a brief application of a result discussed in the last post about the existence of odd ways to map the fundamental group of the Hawaiian earring onto an arbitrary finite group : Theorem 1: Let be any nontrivial finite group and be a loop … Continue reading
Homomorphisms from the earring group to finite groups
One of the the surprising things about the earring group (the fundamental group of the earring space ) is that the group of homomorphisms to the additive group of integers is countable (see this post for details) even though is … Continue reading
Posted in earring group, earring space, Finite groups, Fundamental group, Group homomorphisms, Ultrafilter
Tagged anomalous, axiom of choice, cardinality, epimorphism, filter, finite group, fundamental group, Hawaiian earring, homomorphism, integers, nonprincipal ultrafilter, StoneCech compactification, uncountable
1 Comment
The Uncountability of the Harmonic Archipelago Group
In a previous post, we discussed the fundamental group of the harmonic archipelago in some detail. One item that I skipped earlier is the fact that this group is uncountable. In this post, we’ll see why is uncountable. We’ll use … Continue reading