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