Archives
- November 2025
- November 2024
- September 2024
- October 2023
- April 2023
- February 2023
- 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
- core of a subgroup
- coreflection functor
- Covering Space Theory
- Dendrite
- earring group
- earring space
- Examples
- Finite groups
- first uncountable ordinal
- 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
- Inverse Limits
- locally n-connected spaces
- locally path connected
- one-dimensional spaces
- Order Theory
- path components
- Peano continuum
- Quasitopological groups
- quasitopological groups
- quotient topology
- reduced paths
- reflection functor
- semicovering
- Shape homotopy group
- Shape theory
- Simplicial complexes
- Singular homology
- topological fundamental group
- Topological groups
- Tree
- Ultrafilter
- Uncategorized
Tweets
Tweets by jtbrazas-
This work is licensed under a Creative Commons Attribution 4.0 International License.
Category Archives: earring group
The Baer-Specker Group
One of the infinite abelian groups that is important to infinite abelian group theory and which has shown up naturally in previous posts on infinitary fundamental groups is the Baer-Specker group, often just called the Specker group. This post isn’t … 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 