Infinite games and chain conditions

Santi Spadaro¹

¹ Instituto de Matemática e Estatística (IME-USP) Universidade de São Paulo Rua do Matão, 1010 – Cidade Universitária 05508-090 São Paulo – SP, Brazil

Fundamenta Mathematicae, Tome 234 (2016) no. 3, pp. 229-239

Résumé

We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the $G_\delta $ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak Lindelöf property, every cover by $G_\delta $ sets has a continuum-sized subcollection whose union is $G_\delta $-dense.

Détail

DOI : 10.4064/fm232-3-2016

Keywords: apply theory infinite two person games well known problems topology suslin problem arhangel skii problem weak lindel number delta topology compact space specifically prove results which following special cases every linearly ordered topological space satisfying game theoretic version countable chain condition separable every compact space satisfying game theoretic version weak lindel property every cover delta sets has continuum sized subcollection whose union delta dense