On Open-Open Games of Uncountable Length
The aim of this paper is to investigate the open-open game of uncountable length. We introduce a cardinal number 𝜇(𝑋), which says how long the Player I has to play to ensure a victory. It is proved that 𝑐(𝑋)≤𝜇(𝑋)≤𝑐(𝑋)+. We also introduce the class 𝒞𝜅 of topological spaces that can be represented as...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/208693 |
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| author | Andrzej Kucharski |
| author_facet | Andrzej Kucharski |
| author_sort | Andrzej Kucharski |
| collection | DOAJ |
| description | The aim of this paper is to investigate the open-open
game of uncountable length. We introduce a cardinal number 𝜇(𝑋), which says how long the Player I has to play to ensure a victory. It is proved that 𝑐(𝑋)≤𝜇(𝑋)≤𝑐(𝑋)+. We also introduce the class 𝒞𝜅 of topological spaces that can be represented as the inverse
limit of 𝜅-complete system {𝑋𝜎,𝜋𝜎𝜌,Σ} with 𝑤(𝑋𝜎)≤𝜅 and
skeletal bonding maps. It is shown that product of spaces which
belong to 𝒞𝜅 also belongs to this class and 𝜇(𝑋)≤𝜅 whenever 𝑋∈𝒞𝜅. |
| format | Article |
| id | doaj-art-9ef8c545bab5481f8e8e2b0dacb94704 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9ef8c545bab5481f8e8e2b0dacb947042025-02-03T01:30:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/208693208693On Open-Open Games of Uncountable LengthAndrzej Kucharski0Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, PolandThe aim of this paper is to investigate the open-open game of uncountable length. We introduce a cardinal number 𝜇(𝑋), which says how long the Player I has to play to ensure a victory. It is proved that 𝑐(𝑋)≤𝜇(𝑋)≤𝑐(𝑋)+. We also introduce the class 𝒞𝜅 of topological spaces that can be represented as the inverse limit of 𝜅-complete system {𝑋𝜎,𝜋𝜎𝜌,Σ} with 𝑤(𝑋𝜎)≤𝜅 and skeletal bonding maps. It is shown that product of spaces which belong to 𝒞𝜅 also belongs to this class and 𝜇(𝑋)≤𝜅 whenever 𝑋∈𝒞𝜅.http://dx.doi.org/10.1155/2012/208693 |
| spellingShingle | Andrzej Kucharski On Open-Open Games of Uncountable Length International Journal of Mathematics and Mathematical Sciences |
| title | On Open-Open Games of Uncountable Length |
| title_full | On Open-Open Games of Uncountable Length |
| title_fullStr | On Open-Open Games of Uncountable Length |
| title_full_unstemmed | On Open-Open Games of Uncountable Length |
| title_short | On Open-Open Games of Uncountable Length |
| title_sort | on open open games of uncountable length |
| url | http://dx.doi.org/10.1155/2012/208693 |
| work_keys_str_mv | AT andrzejkucharski onopenopengamesofuncountablelength |