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# 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

## 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

## 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