Tag Archives: quotient space

Topologized Fundamental Groups: The Quotient Topology Part 3 (Why isn’t it always a topological group?)

Posted on April 18, 2023 by Jeremy Brazas

In Part 1, I mentioned that one of the surprising things about the natural quotient topology on the fundamental group is that the resulting group with topology often fails to be a topological group. In fact, I’d say it’s usually … Continue reading →

Posted in compact-open topology, earring group, Free groups, Fundamental group, quotient topology, topological fundamental group, Topological groups, Uncategorized | Tagged , , , , , , , , , , | 5 Comments

The locally path-connected coreflection (Part III)

Posted on December 6, 2014 by Jeremy Brazas

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