Category Archives: Dendrite

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

Homotopically Reduced Paths (Part III)

Posted on December 26, 2020 by Jeremy Brazas

In this last post about reduced paths, I’m going to work through the details of one of the most useful results in wild topology. Writing this post helped me work out my own way of proving this result and hopefully … Continue reading →

Posted in Algebraic Topology, Dendrite, Fundamental group, Fundamental groupoid, Homotopy theory, Inverse Limit, one-dimensional spaces, reduced paths | Leave a comment

Shape injectivity of the earring space (Part II)

Posted on August 6, 2019 by Jeremy Brazas

This is the sequel to Shape injectivity of the earring space (Part I) We’re on our way to proving the canonical homomorphism from the earring group to the inverse limit of free groups is injective. Part I was mostly dedicated … Continue reading →

Posted in Dendrite, earring group, earring space, Free groups, Fundamental group, Inverse Limit, Peano continuum, Shape theory, Tree | 3 Comments