Category Archives: Hawaiian earring

Homotopically Hausdorff Spaces II

In my first post on homotopically Hausdorff spaces, I wrote about the property which describes the existence of loops that can be deformed into arbitrarily small neighborhoods but which are not actually null-homotopic, i.e. can’t be deformed all the way back … Continue reading

Posted in Algebraic Topology, Fundamental group, Group homomorphisms, harmonic archipelago, Hawaiian earring | Tagged , , | Leave a comment

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 wild fundamental groups is the Baer-Specker group, often just called the Specker group. This post isn’t all … Continue reading

Posted in Baer-Specker group, Free abelian groups, Free groups, Group homomorphisms, Hawaiian earring, Infinite Group Theory | Tagged , , , , , , | Leave a comment

Homomorphisms from the Hawaiian earring group to finite groups

One of the the surprising things about the Hawaiian earring group (the fundamental group of the Hawaiian earring space ) is that the group of homomorphisms to the additive group of integers is countable (see this post for details) even though … Continue reading

Posted in Finite groups, Fundamental group, Hawaiian earring, Ultrafilter | Tagged , , , , , , , , , , , , | 1 Comment