Vietoris continuous selections on scattered spaces

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概要

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• We prove that a countable regular space has a continuous selection if D 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 Lindelöf linearly ordered spaces.

• 社団法人 日本数学会の論文

著者

• Fujii Seiji

  Yuge National College Of Maritime Technology

• Miyazaki Kazumi

  Department Of Mathematical Sciences Faculty Of Sciences Ehime University

• Nogura Tsugunori

  Department Of Mathematical Sciences Faculty Of Sciences Ehime University

関連論文

• Vietoris continuous selections on scattered spaces
• Ultrafilters in a product of spaces
• Tightness of compact Hausdorff spaces and normality of product spaces
• COUNTABLY INFINITE PRODUCTS OF SEQUENTIAL TOPOLOGIES

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