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weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces
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 $\kappa = \kappa ^\omega$.
[CN] Comfort W.W., Negrepontis S.: The Theory of Ultrafilters. Springer-Verlag, Berlin-Heidelberg-New York Heidelberg (1974). MR 0396267 | Zbl 0298.02004
[Eck] Eckertson F.: Sums, products and mappings of weakly pseudocompact spaces. Topology Appl. 72 (1996), 149-157. MR 1404273 | Zbl 0857.54022
[Eng] Engelking R.: General Topology. PWN Warszawa (1977). MR 0500780 | Zbl 0373.54002
[GG] García-Ferreira S., García-Máynez A.: On weakly pseudocompact spaces. Houston J. Math. 20 (1994), 145-159. MR 1272568
[GFS] García-Ferreira S., Sanchis M.: On $C$-compact subsets. Houston J. Math. 23 (1997), 65-86. MR 1688689
[NR] Nyikos P., Reichel H.C.: On the structure of zero-dimensional spaces. Indag. Math. 37 (1975), 120-136. MR 0365527
[OT] Okunev O., Tamariz-Mascarúa A.: Generalized linearly ordered spaces and weak pseudocompactness. Comment. Math. Univ. Carolinae 38.4 (1997), 775-790. MR 1603718
[U] Ünlü Y.: Lattices of compactifications of Tychonoff spaces. Topology Appl. 9 (1978), 41-57. MR 0487980
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