Selective versions of chain condition-type properties

TL;DR

This paper investigates selective and game-theoretic variants of classical topological properties such as the ccc, weak Lindel"ofness, and separability, providing characterizations and exploring their relationships with continuum cardinal invariants.

Contribution

It introduces and analyzes new selective and game-theoretic versions of classical properties, linking them to cardinal invariants of the continuum.

Findings

Characterizations of selective and game-theoretic properties

Connections between these properties and continuum cardinal invariants

Insights into the structure of topological spaces with these properties

Abstract

We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal invariants of the continuum.