Author Archives: Jeremy Brazas

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

The locally path-connected coreflection III

This post gives another look at the locally path-connected coreflection that I’ve found quite interesting and useful. We’re motivated by the following two basic observations. Lemma 1: The topological sum of a family of locally path-connected spaces is locally path-connected. Lemma 2: The quotient of a locally … Continue reading

Posted in Categorical Topology, Category Theory, coreflection functor, locally path connected | Tagged , , , , | 3 Comments