Szymon Plewik

TL;DR: In this article, it was shown that a compact space is I-favorable if and only if it can be represented as the limit of a σ-complete inverse system of compact metrizable spaces with skeletal bonding maps.

TL;DR: In this paper, the authors consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces from [P Daniels, K Kunen, H Zhou, On the open open game, Fund Math 145 (3) (1994) 205-220] and [D Fremlin, T Natkaniec, I Reclaw, Universally KUlam Spaces] topological arguments are extracted to show that: every I-favorable space is universally KU, Theorem 8; if a compact space Y is I-avorable, then

TL;DR: In this article, a generalized version of Helly's theorem in terms of monotone functions on linearly ordered sets is presented, and it is shown that the cardinal number responsible for this generalization is exactly the splitting number.

TL;DR: A compact space X is I-favorable if, and only if X can be representing as a limit of a complete inverse system of compact metrizable spaces with skeletal bonding maps as mentioned in this paper.