On Open-Open Games of Uncountable Length

Andrzej Kucharski

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-11

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 .

Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2012/208693.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2012/208693.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:208693

DOI: 10.1155/2012/208693

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().