Infinite games and chain conditions

• Autorzy: Santi Spadaro
• Języki publikacji: EN

Abstrakty

EN

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 $G_{δ}$ 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 $G_{δ}$ sets has a continuum-sized subcollection whose union is $G_{δ}$-dense.

Kategorie tematyczne

• 91A44: Games involving topology or set theory
• 54G10: P -spaces
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 234
• Numer: 3
• Strony: 229-239

Daty

wydano

2016

Twórcy

autor

Santi Spadaro

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

Identyfikatory

DOI

10.4064/fm232-3-2016