Tag Archives: Inverse Limit

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 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