Category Archives: Shape theory

Inverse limits of planar Peano continua are not always planar

Posted on November 5, 2025 by Jeremy Brazas

Recently, I ran into a situation where I had an inverse sequence of *planar Peano continua. I wondered naively if the limit of such a sequence always had to be planar. It turns out the answer is no, even in … Continue reading →

Posted in Cech expansion, General topology, Inverse Limits, one-dimensional spaces, Peano continuum | Tagged , , , , , | 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

Shape injectivity of the earring space (Part I)

Posted on July 31, 2019 by Jeremy Brazas

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 earring space, Free groups, Fundamental group, Inverse Limit, Shape homotopy group, Shape theory, Tree | Tagged , , , , , | 9 Comments