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weakly pseudocompact spaces; GLOTS; compactifications
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].
[Eck] Eckertson F.: Sums, products and mappings of weakly pseudocompact spaces. Topol. Appl. 72 (1996), 149-157. MR 1404273 | Zbl 0857.54022
[Eng] Engelking R.: General Topology. Heldermann Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[GG] García-Ferreira S., García-Máynez A.S.: On weakly pseudocompact spaces. Houston J. Math. 20 (1994), 145-159. MR 1272568
[EO] Eckertson F., Ohta H.: Weak pseudocompactness and zero sets in pseudocompact spaces. manuscript. Zbl 0876.54013
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