Category Archives: General topology

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

The locally path-connected coreflection (Part II)

In the last post, I discussed how to efficiently change the topology of a space in order to obtain a locally path-connected space without changing the homotopy or (co)homology groups of the space in question. This is a handy thing … Continue reading

Posted in Category Theory, General topology | Tagged , , | 5 Comments

The locally path-connected coreflection (Part I)

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 , , , , , , , | 15 Comments