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Tweets
Tweets by jtbrazas-
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Category Archives: Categorical Topology
Topological Group Reflections: turning a group with topology into a topological group, Part II
In Part I, we discussed the operation , which takes in a group equipped with a topology (that does not necessarily interact nicely with the operations of the group) and outputs a topological group. The underlying group of is the … Continue reading
Posted in Categorical Topology, Category Theory, General topology, quasitopological groups, quotient topology, reflection functor, Topological groups, Uncategorized
Tagged categorical topology, category, continuous homomorphism, functor, quasitopological group, reflection functor, topological group, transfinite induction
3 Comments
Topological Group Reflections: turning a group with topology into a topological group, Part I
The main complicating factor with the quotient topology on the fundamental group is that it often fails to be a topological group. More generally, if is a topological monoid and the quotient space is group by a relation that preserves … Continue reading
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
Wild Topology 