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Some results and problems about weakly pseudocompact spaces. (English) Zbl 1037.54503

Summary: A space \(X\) is {truly weakly pseudocompact} if \(X\) is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with \(\chi (x,X)>\omega \) for every \(x\in X\); (2) every locally bounded space is truly weakly pseudocompact; (3) for \(\omega < \kappa <\alpha \), the \(\kappa \)-Lindelöfication of a discrete space of cardinality \(\alpha \) is weakly pseudocompact if \(\kappa = \kappa ^\omega \).

MSC:

54D30 Compactness
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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