Tag Archives: harmonic archipelago

The Griffiths Twin Cone

Posted on June 28, 2014 by Jeremy Brazas

This post is about an important wild space which, in many ways, is similar to the harmonic archipelago space that I posted about a few weeks ago. The Griffiths twin cone (or Griffiths space) was first studied by H.B. Griffiths in the 1950’s … Continue reading →

Posted in Algebraic Topology, earring space, Fundamental group, Griffiths twin cone | Tagged , , , , , | 7 Comments

Homomorphisms from the harmonic archipelago group to finite groups

Posted on June 8, 2014 by Jeremy Brazas

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

The Uncountability of the Harmonic Archipelago Group

Posted on May 23, 2014 by Jeremy Brazas

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