Geodesic
Some results and problems about weakly pseudocompact spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 155-173

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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 $\kappa = \kappa ^\omega$.
Classification : 54D30, 54D35, 54F05
Keywords: weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces 
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Okunev, Oleg; Tamariz-Mascarúa, Angel. Some results and problems about weakly pseudocompact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 155-173. http://geodesic.mathdoc.fr/item/CMUC_2000__41_1_a14/