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# 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

## 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

## 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