Monthly Archives: October 2023

Local n-connectivity vs. the LC^n Property, Part 2

Posted on October 17, 2023 by Jeremy Brazas

In Part 1, I defined local n-connectivity, which says that a space has a basis of n-connected open sets, and the porperty, which says that for all , “small” maps from the -sphere contract using “small” homotopies of “relatively the … Continue reading →

Posted in Algebraic Topology, Examples, General topology, Higher Homotopy groups, Homotopy theory, locally n-connected spaces, locally path connected, Peano continuum, Uncategorized | Tagged , , , , , , | Leave a comment

Local n-connectivity vs. the LC^n Property, Part I

Posted on October 8, 2023 by Jeremy Brazas

I’m going to take a little break from the topologized fundamental group series for a bit. That’s a long series and a distraction might be nice. Right now, I’m going to share a little about a property I’ve been running … Continue reading →

Posted in Dendrite, first uncountable ordinal, Higher Homotopy groups, locally path connected, one-dimensional spaces, path components | Tagged , , , , , | 1 Comment

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