# Alan Dow: An application of ZFC to Topology

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.

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