Vietoris continuous selections on scattered spaces

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Author(s)

Abstract

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.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 54(2), 273-281, 2002-04

    The Mathematical Society of Japan

References:  12

Codes

  • NII Article ID (NAID)
    10008204921
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    6153447
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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