Banach-Mazur game and open mapping theorem

TL;DR

This paper explores a variant of the Banach-Mazur game and its applications to the open mapping theorem, providing insights into topological properties through game-theoretic methods.

Contribution

Introduces a new variant of the Banach-Mazur game and demonstrates its relevance to the open mapping and closed graph theorems in topology.

Findings

Establishes connections between game variants and topological theorems

Provides a new perspective on open mapping theorem proofs

Suggests potential for game-theoretic approaches in topology

Abstract

We discuss a variant of the Banach-Mazur game which has applications to topological open mapping and closed graph theorems.