Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland
Copyright © 2012 Andrzej Kucharski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The aim of this paper is to investigate the open-open
game of uncountable length. We introduce a cardinal number , which says how long the Player I has to play to ensure a victory. It is proved that . We also introduce the class of topological spaces that can be represented as the inverse
limit of -complete system with and
skeletal bonding maps. It is shown that product of spaces which
belong to also belongs to this class and whenever .