Tag Archives: locally path-connected

Topologized Fundamental Groups: The Quotient Topology Part 2 (Discreteness)

Posted on February 13, 2023 by Jeremy Brazas

In Part 1, I described the construction of , the fundamental group equipped with the quotient topology and some of the drama around failing to always be a topological group. In this second post, I plan to connect back to … Continue reading →

Posted in Fundamental group, Uncategorized | Tagged , , , | 4 Comments

The locally path-connected coreflection (Part II)

Posted on November 6, 2014 by Jeremy Brazas

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)

Posted on October 11, 2014 by Jeremy Brazas

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