A space $X$ is {\it truly weakly pseudocompact} if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove that if $X$ is a generalized linearly ordered space, and either (i) each proper open interval in $X$ is truly weakly pseudocompact, or (ii) $X$ is paracompact and each point of $X$ has a truly weakly pseudocompact neighborhood, then $X$ is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].
@article{118972,
author = {Oleg Okunev and Angel Tamariz-Mascar\'ua},
title = {Generalized linearly ordered spaces and weak pseudocompactness},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {38},
year = {1997},
pages = {775-790},
zbl = {0937.54021},
mrnumber = {1603718},
language = {en},
url = {http://dml.mathdoc.fr/item/118972}
}
Okunev, Oleg; Tamariz-Mascarúa, Angel. Generalized linearly ordered spaces and weak pseudocompactness. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 775-790. http://gdmltest.u-ga.fr/item/118972/
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