When is a Pixley-Roy hyperspace CCC? |
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Authors: | A Hajnal I Juhász |
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Institution: | Magyar Tudományos Akadémia Matematikai Kutató Intézete, Budapest, Hungary |
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Abstract: | A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω1, any family of open subsets of Y with ||=ω1 has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace X] is CCC. We show that under MAω1 condition (C) is also necessary for X] to be CCC, but under CH it is not. |
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Keywords: | 54B20 54A25 03E35 Pixley-Roy hyperspace CCC MA CH |
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