Place: Fields Institute (Room 210)
Date: September 25th, 2015 (13:30-15:00)
Speaker: Alan Dow
Title: An application of ZFC to Topology
Abstract: A space X is said to be M-dominated for a metric space M if there is a covering of X by compact sets that is order-preservingly indexed by the compact subsets of M. Of special interest is when M is the irrationals, we may denote as P. This gave rise to a question by Cascales, Orihuela, and Tkachuk as to whether a compact space with a P-diagonal (defined as $X^2$ minus the diagonal is P dominated) is metrizable. Following up on their results that a YES answer holds if X has countable tightness, and further a YES answer follows from assuming that the bounding number is greater than $\omega_1$, we earlier proved with David Guerrero Sanchez, that CH also implies a YES answer. We report on a new result, with K.P. Hart, that the answer is YES in ZFC.