Open-point topological games and productivity of dense-separable property

zbMATH Open1357.54005arXiv1506.06080MaRDI QIDQ2954185

Publication date: 12 January 2017

Abstract: In this note we study the open-point topological games in order to analyze the least upper bound for density of dense subsets of a topological space. This way we may also analyze the behavior of such cardinal invariants in taking products of spaces. Various related cardinal equalities and inequalities are given. As an application we take a look at Banach spaces with the property (CSP) which can be formulated by stating that each weak-star dense linear subspace of the dual is weak-star separable.

Full work available at URL: https://arxiv.org/abs/1506.06080

zbMATH Keywords

productivity weight product space hereditarily separable \(\pi\)-weight \(L\) space \(S\) space dense-separable open-point game

Mathematics Subject Classification ID

Games involving topology, set theory, or logic (91A44) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Nonseparable Banach spaces (46B26) Base properties of topological spaces (54D70) Separability of topological spaces (54D65) Determinacy principles (03E60)

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