Resolvability of topological spaces
A topological space is called resolvable if it is the union of two disjoint dense subsets. Since the concept was first defined and explored by Edwin Hewitt in 1943, much effort has been invested in obtaining general results concerning the resolvability or irresolvability of certain types of spaces, and in generating examples and counterexamples.
In the present lecture we will take a leisurely tour through the subject. We will discuss generalizations of the original concept, display some of the results obtained throughout the years and mention questions which are still open.