Monthly Archives: December 2020

Homotopically Reduced Paths (Part III)

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)

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)

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