Pointless proofs of the Menger and Rothberger games

TL;DR

This paper provides point-free proofs for key theorems in topological game theory, specifically Hurewicz's and Pawlikowski's theorems, within the framework of lattices.

Contribution

It introduces a novel point-free approach to proving fundamental theorems in topological games, expanding the methods beyond point-based arguments.

Findings

Point-free proofs of Hurewicz's and Pawlikowski's theorems

Extension of topological game theory to lattice frameworks

Simplification of proofs by avoiding point-based reasoning

Abstract

This work presents proofs for Hurewicz's and Pawlikowski's Theorems about topological games in the context of lattices, in which one cannot argue with points.