Relating games of Menger, countable fan tightness, and selective separability

TL;DR

This paper explores the relationships between various selection games in topology, demonstrating equivalences of strategies and addressing Gruenhage's question about different forms of selective separability.

Contribution

It adapts existing techniques to establish strategy equivalences in selection games, providing insights into the nature of selectively separable spaces.

Findings

Equivalence of perfect-information, Markov, and tactical strategies in certain selection games

Addresses Gruenhage's question on Markov selectively separable spaces

Provides new connections between game-theoretic and topological properties

Abstract

By adapting techniques of Arhangel'skii, Barman, and Dow, we may equate the existence of perfect-information, Markov, and tactical strategies between two interesting selection games. These results shed some light on Gruenhage's question asking whether all strategically selectively separable spaces are Markov selectively separable.