Category Archives: Inverse Limit

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

Shape injectivity of the earring space (Part II)

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, Free groups, Fundamental group, Hawaiian earring, Inverse Limit, Peano continuum, Shape theory, Tree, Uncategorized | 3 Comments

Shape injectivity of the earring space (Part I)

One of my posts where I did some substantial hand-waving is my original post on the fundamental group of the earring space. I wrote about how to understand and work with this group, but I never gave a proof of … Continue reading

Posted in Free groups, Fundamental group, Hawaiian earring, Inverse Limit, Tree | 8 Comments