Category Archives: Cech expansion

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

The Cech Expansion: nerves of open covers

The Whitehead theorem in homotopy theory basically says that to fully understand the homotopy type of a CW-complex one only needs to know about the homotopy groups (really, the weak homotopy type). It is very easy to produce spaces to … Continue reading

Posted in Cech expansion, Shape theory, Simplicial complexes | Tagged , , , , , | 4 Comments