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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |