Category Archives: one-dimensional spaces

Inverse limits of planar Peano continua are not always planar

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

Local n-connectivity vs. the LC^n Property, Part I

I’m going to take a little break from the topologized fundamental group series for a bit. That’s a long series and a distraction might be nice. Right now, I’m going to share a little about a property I’ve been running … Continue reading

Posted in Dendrite, first uncountable ordinal, Higher Homotopy groups, locally path connected, one-dimensional spaces, path components | Tagged , , , , , | 1 Comment

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