## 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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