Category Archives: Algebraic Topology

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

Say you’ve got some path-connected space and you want to know about it’s fundamental group . But isn’t locally path-connected so pretty much any standard tools in algebraic topology aren’t going to help you out. What’s an algebraic topologist to … Continue reading

Posted in Algebraic Topology, Category Theory, General topology | Tagged , , , , , , , | 3 Comments