Monthly Archives: December 2020

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

Homotopically Reduced Paths (Part II)

Posted on December 23, 2020 by Jeremy Brazas

Understanding this post requires reading Part I where I explain what reduced paths are and how we might go about proving they exist. In this second part, I’ll go into detail about how to use Zorn’s lemma to identifying a … Continue reading →

Posted in Fundamental groupoid, reduced paths | Tagged , , , , , , , | 1 Comment

Homotopically Reduced Paths (Part I)

Posted on December 18, 2020 by Jeremy Brazas

The topic of this post focuses on a general concept that is heavily used in the wild topology world. Writing this post has been a fun exploration I’ve been meaning to spend time on for a while now. I will … Continue reading →

Posted in Fundamental group, Homotopy theory | Tagged , | 2 Comments