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Oleg Okunev, Angel Tamariz-Mascar´ ua

Some results and problems about weakly pseudocompact spaces

Comment.Math.Univ.Carolinae 41,1 (2000) 155-173.

Abstract: A spaceX is truly weakly pseudocompact ifX is either weakly pseudo- compact or Lindel¨of locally compact. We prove: (1) every locally weakly pseudo- compact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with χ(x, X)> ω for everyx∈X; (2) every locally bounded space is truly weakly pseudocompact; (3) forω < κ < α, theκ-Lindel¨ofication of a discrete space of cardinalityαis weakly pseudocompact ifκ=κω.

Keywords: weakly pseudocompact spaces, GLOTS, compactifications, locally bounded spaces, proto-metrizable spaces

AMS Subject Classification: 54D35, 54F05

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