Universally Kuratowski-Ulam spaces and open-open games

TL;DR

This paper investigates the properties of spaces where the second player can win the open-open game, revealing they are not universally Kuratowski-Ulam, and compares two game variants, G and G7, showing they are not equivalent.

Contribution

It demonstrates that spaces with a winning second player in the open-open game are not universally Kuratowski-Ulam and clarifies the non-equivalence of two game variants G and G7.

Findings

Spaces with a winning second player are not universally Kuratowski-Ulam

Games G and G7 are not equivalent

Provides insights into the structure of open-open games

Abstract

We examine the class of spaces in which the second player has a winning strategy in the open--open game. We show that this spaces are not universally Kuratowski-Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205--220] are not equivalent.