Game Approach to Universally Kuratowski-Ulam Spaces

Details Game Approach to Universally Kuratowski-Ulam Spaces Game Approach to Universally Kuratowski-Ulam Spaces

2006-05-17

arxiv.org/abs/math/0605469v1

Mathematics

General Topology

The paper is accepted for publication in "Topology and its Applications." (12 pages)

Scientific paper

We consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable, then the hyperspace exp(Y) with the Vietoris topology is I-favorable, and hence universally Kuratowski-Ulam, (Theorems 6 and 9). Notions of uK-U and uK-U* spaces are compared.

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