Tag Archives: uncountable

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

Posted in Cardinality, Finite groups, Fundamental group, harmonic archipelago | Tagged , , , , , | Leave a comment

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

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

Posted in Baer-Specker group, Fundamental group, harmonic archipelago | Tagged , , , , , , , | 1 Comment