Set-theoretic topology is a branch of topology in which set- theoretic techniques are used to solve problems about abstract spaces. In it, special axioms (such as Godel's Axiom of Constructibility, the Continuum Hypothesis, Martin's Axiom, and the Proper Forcing Axiom), forcing techniques, inner model theory, and other set theoretic tools are used to clarify, and often solve, long-outstanding problems, and to isolate and identify topological properties worthy of study. The investigator will continue his research in this area. The research will focus on two primary topics and four secondary topics which show particular promise in the light of recent results by the investigator and others. The two primary topics are hereditary normality and sequential compactness, where it is hoped that recent successes with the topic of countable tightness can be extended and paralleled. The secondary topics are: locally compact spaces of small size, Frechet-Urysohn topological groups and vector spaces, nonmetrizable manifolds, and countable intersections of open sets in countably metacompact spaces.
