Author Archives: Jeremy Brazas

Homotopically Hausdorff Spaces (Part II)

In my post homotopically Hausdorff spaces (Part I), 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, earring space, Fundamental group, Group homomorphisms, harmonic archipelago, homotopically Hausdorff, Homotopy theory | Tagged , , , | 2 Comments

Homotopically Hausdorff Spaces (Part 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 , , , | 3 Comments

The locally path-connected coreflection (Part III)

This post gives another look at the locally path-connected coreflection that I’ve found quite interesting and useful. For the previous posts see Part I and Part II. In this post, we’ll be motivated by the following two basic observations. Lemma … Continue reading

Posted in Categorical Topology, Category Theory, coreflection functor, locally path connected | Tagged , , , , | 8 Comments