Douglas L. Grant - Alternative universes: the role of set theory in topological algebra

This survey will explore some of the theorems of topological algebra in which significantly more powerful results are available than in the analagous case for Hausdorff spaces. In addition, some cases will be considered where the construction of counterexamples has required more powerful set-theoretic assumptions than is the case in general topology. In most of those instances, solutions without set-theoretic axioms beyond ZFC remain open problems.