Vietoris continuous selections on scattered spaces

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN(2002)

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摘要
We prove that a countable regular space has a continuous selection if and only if it is scattered. Further we prove that a paracompact scattered space admits a continuous selection if each of its points has a countable pseudo-base. We also provide two examples to show that: (1) paracompactness can not be replaced by countable compactness even together with (collectionwise) normality, and (2) having countable pseudo-base at each of its points can not be omitted even in the class of regular Lindelof linearly ordered spaces.
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关键词
(co-)stationary set,hereditarily Baire,hyperspace,ordered space,pressing down,scattered,selection
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