Products of Menger spaces

Speaker(s)

Piotr Szewczak; Coauthor: Boaz Tsaban (Bar-Ilan University, Israel)

Affiliation

Cardinal Stefan Wyszyński University in Warsaw

Date

Oct. 14, 2015, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

---

   A topological space X is Menger if for every sequence of open covers O_1, O_2, . . . 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.

---