Selection Games with Minimal Usco Maps

TL;DR

This paper explores topological selection games involving minimal usco maps, establishing relationships with continuous function spaces and analyzing various game types under different topologies.

Contribution

It introduces new connections between selection games on minimal usco maps and classical function space results, considering full- and limited-information strategies.

Findings

Relationships between selection games and topologies of minimal usco maps

Connections to classical function space selection game results

Analysis of strategies in various topological contexts

Abstract

We establish relationships between various topological selection games involving the space of minimal usco maps with various topologies, including the topology of pointwise convergence and the topology of uniform convergence on compact sets, and the underlying domain using full- and limited-information strategies. We also tie these relationships to analogous results related to spaces of continuous functions. The primary games we consider include Rothberger-like games, generalized point-open games, strong fan-tightness games, Tkachuk's closed discrete selection game, and Gruenhage's $W$-games.