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On Open-Open Games of Uncountable Length

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  • Andrzej Kucharski

Abstract

The aim of this paper is to investigate the open-open game of uncountable length. We introduce a cardinal number 𠜇 ( ð ‘‹ ) , which says how long the Player I has to play to ensure a victory. It is proved that ð ‘ ( ð ‘‹ ) ≤ 𠜇 ( ð ‘‹ ) ≤ ð ‘ ( ð ‘‹ ) + . We also introduce the class ð ’ž 𠜅 of topological spaces that can be represented as the inverse limit of 𠜅 -complete system { ð ‘‹ 𠜎 , 𠜋 𠜎 𠜌 , Σ } with 𠑤 ( ð ‘‹ 𠜎 ) ≤ 𠜅 and skeletal bonding maps. It is shown that product of spaces which belong to ð ’ž 𠜅 also belongs to this class and 𠜇 ( ð ‘‹ ) ≤ 𠜅 whenever ð ‘‹ ∈ ð ’ž 𠜅 .

Suggested Citation

  • Andrzej Kucharski, 2012. "On Open-Open Games of Uncountable Length," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, July.
    • Handle: RePEc:hin:jijmms:208693
    DOI: 10.1155/2012/208693
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