Contents V.9, N.2, 2018

  • ON C∗ u − AND Cu− EMBEDDED UNIFORM SPACES
    ASYLBEK CHEKEEV, BAKTIYAR RAKHMANKULOV, AIGUL CHANBAEVA (pp. 173-189)
  • Abstract

    For a uniform space uX the concept of Cu-embedding (C ∗ u-embedding) in some uniform space is introduced. An analogue of Urysohn’s Theorem is proved and it is established, that uX is C ∗ u 􀀀embedded in the Wallman 􀀀like compactification uX, and any compactification of uX in which uX is C ∗ u 􀀀embedded, must be uX. A uniformly realcompact space is determined. It is proved, that uX is Cu􀀀embedded in the Wallman realcompactification uX, and any uniform realcompactification in which uX is Cu􀀀embedded, is uX.

    Keywords

    u-open (closed) sets, zu-filter, zu-ultrafilter, coz-mapping, u-continuous function, Wallman b-like compactification, Wallman realcompactification.

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