Limited Information Strategies and Discrete Selectivity

TL;DR

This paper explores the relationship between discrete selectivity, limited information strategies, and topological properties, establishing equivalences between game-theoretic and classical topological concepts.

Contribution

It connects discrete selectivity and limited information strategies in topological function spaces to well-known topological properties and game-theoretic frameworks.

Findings

Player II can win the discrete selection game on C_p(X) iff they can win a point open game on X.

Existence of limited information strategies in the discrete selection game is equivalent to known topological properties.

The paper establishes equivalences between game-theoretic strategies and classical topological concepts.

Abstract

We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuck, to a variety of selection principles and point picking games. In particular we show that player II can win the discrete selection game on \(C_p(X)\) if and only if player II can win a variant of the point open game on \(X\). We also show that the existence of limited information strategies in the discrete selection game on \(C_p(X)\) for either player are equivalent to other well-known topological properties.