Archives
Categories
 Algebraic Topology
 BaerSpecker group
 Cardinality
 Categorical Topology
 Category Theory
 Conferences
 coreflection functor
 Covering Space Theory
 Dendrite
 earring group
 earring space
 Examples
 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
 Hawaiian earring
 Higher Homotopy groups
 Homotopy theory
 Infinite Group Theory
 Infinite products
 Inverse Limit
 locally path connected
 onedimensional spaces
 Order Theory
 Peano continuum
 reduced paths
 semicovering
 Shape theory
 Simplicial complexes
 Singular homology
 Tree
 Ultrafilter
 Uncategorized
Tweets
 I taught for 5 years at GSU as a lecturer. The student population, which is primarily Black (satellite campuses too… twitter.com/i/web/status/1… 4 days ago
 RT @pwr2dppl: EVERYTHING IS GARBAGE, NOW WHAT? Piper H October 19, 2021 6 days ago
 RT @cbrazas: My @BLMPhilly sign was removed from the yard! It happened Monday night. Who do we think the perpetrators are? 1 week ago
 RT @cbrazas: How in 2021, in the year of our lord Lil Nas X, are "teachers" still using the N word in schools? How are they still not getti… 2 weeks ago
 I had need to think about pushouts of trees this week. How about just pushouts of PLmaps of arcs [0,1]>[0,1]?… twitter.com/i/web/status/1… 2 weeks ago

This work is licensed under a Creative Commons Attribution 4.0 International License.
Monthly Archives: May 2014
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
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 twopart post to convince ourselves that the fundamental group of the earring space … Continue reading
The earring group is not free (Part II)
This post is Part II in an explanation of why the fundamental group of the earring space is not a free group. I’ll be referencing the notation and results that we worked through in Part I. Recall that the earring group is … Continue reading
Posted in Free groups, Fundamental group, Hawaiian earring
Tagged free group, fundamental group, Hawaiian earring, homset, homomorphism, quotient group
5 Comments