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Tag Archives: integers
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, nonprincipal ultrafilter, StoneCech 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 twopart post to convince ourselves that the fundamental group of the earring space … Continue reading
The earring group is not free (Part I)
The main goal of this twopart post will be to study the homomorphisms out of the earring group. Click here to get to Part II. In particular, we’ll end up concluding that the set of homomorphisms to the additive group … Continue reading