A space $X$ is {\it 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 $\kappa = \kappa ^\omega$.
@article{119150,
author = {Oleg Okunev and Angel Tamariz-Mascar\'ua},
title = {Some results and problems about weakly pseudocompact spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {155-173},
zbl = {1037.54503},
mrnumber = {1756936},
language = {en},
url = {http://dml.mathdoc.fr/item/119150}
}
Okunev, Oleg; Tamariz-Mascarúa, Angel. Some results and problems about weakly pseudocompact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 155-173. http://gdmltest.u-ga.fr/item/119150/
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