Andrew Brooke-Taylor (University of Leeds) – Products of CW complexes

CW complexes are topological spaces built up dimension by dimension from Euclidean cells, with a subset declared to be open if its intersection with each of these cells is open. Unfortunately when you take the product of two CW complexes, the product topology does not in general satisfy this requirement. I will explain when exactly it does; it turns out that it depends on the cardinal $\mathfrak{b}$. For the old hands who have seen this talk multiple times before, there will also be something new, with details that I realised last week I ought to draw out more.