Category Archives: semicovering

Topologized Fundamental Groups: The Quotient Topology Part 4 (Subgroup Classifications)

Posted on October 7, 2023 by Jeremy Brazas

This is the last in a sequence of posts about the quotient topology. This one is about how the topological structure of can be used to classify certain generalizations of covering maps for locally complicated spaces. Sometimes it still amazes … Continue reading →

Posted in Algebraic Topology, core of a subgroup, Fundamental group, Generalized covering space theory, Griffiths twin cone, harmonic archipelago, Quasitopological groups, quotient topology, semicovering, topological fundamental group, Uncategorized | 7 Comments

When is a local homeomorphism a semicovering map?

Posted on January 1, 2022 by Jeremy Brazas

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

What is a semicovering map?

Posted on July 19, 2021 by Jeremy Brazas

I’ve heard twice in the past year from folks who study non-Archimedian geometry and have found connections to “semicoverings,” which are a generalization of covering maps used in wild topology. The questions I received had me revisiting the basics and … Continue reading →

Posted in Algebraic Topology, Covering Space Theory, earring space, Fundamental group, Generalized covering space theory, semicovering | Tagged , , , , , , | 2 Comments