Some results and problems about weakly pseudocompact spaces

Oleg Okunev; Angel Tamariz-Mascarúa

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 155-173
  • ISSN: 0010-2628

Abstract

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A space X is 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 χ ( x , X ) > ω for every x ∈ X ; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ < α , the κ -Lindelöfication of a discrete space of cardinality α is weakly pseudocompact if κ = κ ω .

How to cite

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Okunev, Oleg, and Tamariz-Mascarúa, Angel. "Some results and problems about weakly pseudocompact spaces." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 155-173. <http://eudml.org/doc/248594>.

@article{Okunev2000,
abstract = {A space $X$ is 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 $.},
author = {Okunev, Oleg, Tamariz-Mascarúa, Angel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces; weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces},
language = {eng},
number = {1},
pages = {155-173},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results and problems about weakly pseudocompact spaces},
url = {http://eudml.org/doc/248594},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Okunev, Oleg
AU - Tamariz-Mascarúa, Angel
TI - Some results and problems about weakly pseudocompact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 155
EP - 173
AB - A space $X$ is 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 $.
LA - eng
KW - weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces; weakly pseudocompact spaces; GLOTS; compactifications; locally bounded spaces; proto-metrizable spaces
UR - http://eudml.org/doc/248594
ER -

References

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  5. García-Ferreira S., Sanchis M., On C -compact subsets, Houston J. Math. 23 (1997), 65-86. (1997) MR1688689
  6. Nyikos P., Reichel H.C., On the structure of zero-dimensional spaces, Indag. Math. 37 (1975), 120-136. (1975) MR0365527
  7. Okunev O., Tamariz-Mascarúa A., Generalized linearly ordered spaces and weak pseudocompactness, Comment. Math. Univ. Carolinae 38.4 (1997), 775-790. (1997) MR1603718
  8. Ünlü Y., Lattices of compactifications of Tychonoff spaces, Topology Appl. 9 (1978), 41-57. (1978) MR0487980

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