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.

Abstract

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 .