Cardinal Functions in Set-theoretic Topology, I

This is the first lecture in a 3 part series of lectures by William Weiss (U. of Toronto) about set-theoretic topology. The lectures are intended for anyone who is interested in learning about interactions between general topology and set theory. The level is intended for advanced Master's students and Ph.D. students.

Abstract of the first talk: We first introduce some reasons to study zero-dimensional spaces and give some motivating examples. We then introduce a number of cardinal-valued topological invariants called cardinal functions and we survey the many relationships among them. We then look a number of natural questions which cannot be settled using the usual axioms of mathematics.