Previous |  Up |  Next


Title: Some results and problems about weakly pseudocompact spaces (English)
Author: Okunev, Oleg
Author: Tamariz-Mascarúa, Angel
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 1
Year: 2000
Pages: 155-173
Category: math
Summary: 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 $\kappa = \kappa ^\omega$. (English)
Keyword: weakly pseudocompact spaces
Keyword: GLOTS
Keyword: compactifications
Keyword: locally bounded spaces
Keyword: proto-metrizable spaces
MSC: 54D30
MSC: 54D35
MSC: 54F05
idZBL: Zbl 1037.54503
idMR: MR1756936
Date available: 2009-01-08T18:59:38Z
Last updated: 2012-04-30
Stable URL:
Reference: [CN] Comfort W.W., Negrepontis S.: The Theory of Ultrafilters.Springer-Verlag, Berlin-Heidelberg-New York Heidelberg (1974). Zbl 0298.02004, MR 0396267
Reference: [Eck] Eckertson F.: Sums, products and mappings of weakly pseudocompact spaces.Topology Appl. 72 (1996), 149-157. Zbl 0857.54022, MR 1404273
Reference: [Eng] Engelking R.: General Topology.PWN Warszawa (1977). Zbl 0373.54002, MR 0500780
Reference: [GG] García-Ferreira S., García-Máynez A.: On weakly pseudocompact spaces.Houston J. Math. 20 (1994), 145-159. MR 1272568
Reference: [GFS] García-Ferreira S., Sanchis M.: On $C$-compact subsets.Houston J. Math. 23 (1997), 65-86. MR 1688689
Reference: [NR] Nyikos P., Reichel H.C.: On the structure of zero-dimensional spaces.Indag. Math. 37 (1975), 120-136. MR 0365527
Reference: [OT] Okunev O., Tamariz-Mascarúa A.: Generalized linearly ordered spaces and weak pseudocompactness.Comment. Math. Univ. Carolinae 38.4 (1997), 775-790. MR 1603718
Reference: [U] Ünlü Y.: Lattices of compactifications of Tychonoff spaces.Topology Appl. 9 (1978), 41-57. MR 0487980


Files Size Format View
CommentatMathUnivCarolRetro_41-2000-1_15.pdf 297.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo