Category Archives: harmonic archipelago

Homotopically Hausdorff Spaces II

In my first post on homotopically Hausdorff spaces, 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, Fundamental group, Group homomorphisms, harmonic archipelago, Hawaiian earring | Tagged , , | Leave a comment

Homotopically Hausdorff Spaces I

In previous posts, I wrote about the harmonic archipelago  (see also here and here): as well as the Griffiths Twin Cone . One special feature of these 2-dimensional spaces is that any loop either of these spaces can be deformed to lie … Continue reading

Posted in Covering Space Theory, Fundamental group, Griffiths twin cone, harmonic archipelago, Homotopy theory, Uncategorized | Tagged , , , | 1 Comment

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