Category Archives: Group homomorphisms

Homotopically Hausdorff Spaces (Part II)

In my post homotopically Hausdorff spaces (Part I), 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, earring space, Fundamental group, Group homomorphisms, harmonic archipelago, homotopically Hausdorff, Homotopy theory | Tagged , , , | 2 Comments

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

Posted in Baer-Specker group, earring group, earring space, Free abelian groups, Free groups, Group homomorphisms, Infinite Group Theory | Tagged , , , , , , , | 7 Comments

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 , , , , , , , , , , , , | 1 Comment