Game theoretic approach to skeletally Dugundji and Dugundji spaces

TL;DR

This paper characterizes skeletally Dugundji and Dugundji spaces using game-theoretic concepts involving club collections of co-zero sets, providing new topological characterizations.

Contribution

It introduces game-theoretic characterizations of skeletally Dugundji and Dugundji spaces via additive club collections, offering novel topological insights.

Findings

Skeletally Dugundji spaces characterized by additive c-clubs.

Dugundji spaces characterized by additive d-clubs.

Provides new topological characterizations using club collections.

Abstract

Characterizations of skeletally Dugundji spaces and Dugundji spaces are given in terms of club collections, consisting of countable families of co-zero sets. For example, a Tychonoff space $X$ is skeletally Dugundji if and only if there exists an additive $c$-club on $X$. Dugundji spaces are characterized by the existence of additive $d$-clubs.