Author Archives: Jeremy Brazas

Topologized Fundamental Groups: The Whisker Topology, Part 1

Posted in Covering Space Theory, Fundamental group, topological fundamental group, Topological groups | 3 Comments

How to “topologize” the fundamental group: a primer

The fundamental group, from algebraic topology, is one of the most widely used invariants in mathematics. Topological groups, such as pro-finite groups, Lie groups, ordered groups, etc, also arise in many different areas. So it’s natural to ask, can the … Continue reading

Posted in Algebraic Topology, Fundamental group, Topological groups, Uncategorized | Tagged , , , , | 5 Comments

When is a local homeomorphism a semicovering map?

In a previous post “What is a Semicovering Map?,” I gave an introduction to semicovering maps. A semicovering is a slight generalization of covering map that becomes particularly relevant when you’re dealing with locally complicated spaces. In particular, a semicovering … Continue reading

Posted in Algebraic Topology, Covering Space Theory, Fundamental group, Generalized covering space theory, semicovering | Leave a comment