Kurt Gödel Research Center

2016 seminar talk: Products of Menger spaces

Talk held by Piotr Szewczak (Cardinal Stefan Wyszynski University in Warsaw, Poland) at the KGRC seminar on 2016-10-20.

Abstract

A topological space $X$ is Menger if for every sequence of open covers $O_1, O_2,$ $\dots$ there are finite subfamilies $F_1$ of $O_1$, $F_2$ of $O_2,$ $\dots$ such that their union is a cover of $X$. The above property generalizes $\sigma$-compactness. We provide examples of Menger subsets of the real line whose product is not Menger under various set theoretic hypotheses, some being weak portions of the Continuum Hypothesis, and some violating it. The proof method is new.