Oleg Okunev, Angel Tamariz-Mascar\'ua
Some results and problems about weakly pseudocompact spaces

Comment.Math.Univ.Carolinae 41,1 (2000) 155-173.

Abstract:A space $X$ is {truly weakly pseudocompact} if $X$ is either weakly pseudocompact or Lindel\"of 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 $-Lindel\"ofication of a discrete space of cardinality $\alpha $ is weakly pseudocompact if $\kappa = \kappa ^\omega $.

Keywords: weakly pseudocompact spaces, GLOTS, compactifications, locally bounded spaces, proto-metrizable spaces
AMS Subject Classification: 54D35, 54F05