Piotr Szewczak: Products of Menger spaces

Tuesday, November 24, 2015, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)

Coauthor: Boaz Tsaban (Bar-Ilan University)

Title: Products of Menger spaces

Abstract:

A topological space $X$ is Menger if for every sequence of open covers $O_1, O_2,\ldots$ there are finite subfamilies $F_1$ of $O_1$, $F_2$ of $O_2$, . . . such that their union is a cover of $X$. The above property generalizes sigma-compactness.

One of the major open problems in the field of selection principles is whether there are, in ZFC, two Menger sets of real numbers whose product is not Menger. We provide examples under various set theoretic hypotheses, some being weak portions of the Continuum Hypothesis, and some violating it. The proof method is new.

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