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Tag Archives: homomorphism
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
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
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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 