Relatively realcompact sets and nearly pseudocompact spaces

John J. Schommer

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 375-382
  • ISSN: 0010-2628

Abstract

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A space is said to be nearly pseudocompact iff v X - X is dense in β X - X . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.

How to cite

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Schommer, John J.. "Relatively realcompact sets and nearly pseudocompact spaces." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 375-382. <http://eudml.org/doc/247523>.

@article{Schommer1993,
abstract = {A space is said to be nearly pseudocompact iff $vX-X$ is dense in $\beta X-X$. In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.},
author = {Schommer, John J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nearly pseudocompact; nearly realcompact; $G_\delta $-relatively realcompact; relatively realcompact; relatively pseudocompact; relatively compact; nowhere locally compact; nearly pseudocompact space; relatively realcompact space; - relatively realcompact space; Čech-Stone compactification},
language = {eng},
number = {2},
pages = {375-382},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relatively realcompact sets and nearly pseudocompact spaces},
url = {http://eudml.org/doc/247523},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Schommer, John J.
TI - Relatively realcompact sets and nearly pseudocompact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 375
EP - 382
AB - A space is said to be nearly pseudocompact iff $vX-X$ is dense in $\beta X-X$. In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.
LA - eng
KW - nearly pseudocompact; nearly realcompact; $G_\delta $-relatively realcompact; relatively realcompact; relatively pseudocompact; relatively compact; nowhere locally compact; nearly pseudocompact space; relatively realcompact space; - relatively realcompact space; Čech-Stone compactification
UR - http://eudml.org/doc/247523
ER -

References

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  1. Blair R., On v -embedded sets in topological spaces, in ``TOPO 72 - General Topology and its Applications'', Second Pittsburg International Conference, December 18-22, 1972, Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg-New York, 1974, pp. 46-79. MR0358677
  2. Blair R., Spaces in which special sets are z -embedded, Canadian Journal of Math. 28 (1976), 673-690. (1976) Zbl0359.54009MR0420542
  3. Blair R., van Douwen E., Nearly realcompact spaces, Topology Appl. 47, (1992), 209-221. (1992) Zbl0772.54021MR1192310
  4. Blair R., Swardson M.A., Spaces with an Oz Stone-Čech compactification, Topology Appl. 36 (1990), 73-92. (1990) Zbl0721.54018MR1062186
  5. Engelking R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  6. Gillman L., Jerison M., Rings of Continuous Functions, University Series in Higher Math., Van Nostrand, Princeton, 1960. Zbl0327.46040MR0116199
  7. Henriksen M., Rayburn M., On nearly pseudocompact spaces, Topology Appl. 11 (1980), 161-172. (1980) Zbl0419.54009MR0572371
  8. Mrówka S., Functionals on uniformly closed rings of continuous functions, Fund. Math. 46 (1958), 81-87. (1958) MR0100217
  9. Negrepontis S., Baire sets in topological spaces, Arch. Math. 18 (1967), 603-608. (1967) Zbl0152.39703MR0220248
  10. Rayburn M., On hard sets, Topology Appl. 6 (1976), 21-26. (1976) Zbl0323.54022MR0394577
  11. Weir M., Hewitt-Nachbin Spaces, North-Holland Math. Studies 17, North-Holland and American Elsevier, Amsterdam and New York, 1975. Zbl0314.54002MR0514909

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