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/
Sums, products and mappings of weakly pseudocompact spaces, Topol. Appl. 72 (1996), 149-157. (1996) | MR 1404273 | Zbl 0857.54022
General Topology, Heldermann Verlag, Berlin, 1989. | MR 1039321 | Zbl 0684.54001
On weakly pseudocompact spaces, Houston J. Math. 20 (1994), 145-159. (1994) | MR 1272568
Weak pseudocompactness and zero sets in pseudocompact spaces, manuscript. | Zbl 0876.54013