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
- Baer-Specker group
- Cardinality
- Categorical Topology
- Category Theory
- Cech expansion
- compact-open 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
- one-dimensional 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.
Tag Archives: homomorphism
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 non-trivial 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, non-principal ultrafilter, Stone-Cech compactification, uncountable
1 Comment
The Harmonic Archipelago Group is not Free
In recent posts, I’ve been writing about the behavior of fundamental groups of the most fundamental “wild” spaces. We did a decent amount of work in a two-part post to convince ourselves that the fundamental group of the earring space … Continue reading
Wild Topology 