r-Realcompact spaces

D. Bhattacharya; Lipika Dey

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 2, page 253-267
  • ISSN: 0010-2628

Abstract

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A new generalization of realcompactness based on ultrafilters of regular F σ -subsets is introduced. Its relationship with realcompactness, almost realcompactness, almost* realcompactness, c-realcompactness is examined. Some of the properties of the newly introduced space is studied as well.

How to cite

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Bhattacharya, D., and Dey, Lipika. "r-Realcompact spaces." Commentationes Mathematicae Universitatis Carolinae 53.2 (2012): 253-267. <http://eudml.org/doc/246457>.

@article{Bhattacharya2012,
abstract = {A new generalization of realcompactness based on ultrafilters of regular $F_\{\sigma \}$-subsets is introduced. Its relationship with realcompactness, almost realcompactness, almost* realcompactness, c-realcompactness is examined. Some of the properties of the newly introduced space is studied as well.},
author = {Bhattacharya, D., Dey, Lipika},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regular $F_\{\sigma \}$-subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact; regular -subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact},
language = {eng},
number = {2},
pages = {253-267},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {r-Realcompact spaces},
url = {http://eudml.org/doc/246457},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Bhattacharya, D.
AU - Dey, Lipika
TI - r-Realcompact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 2
SP - 253
EP - 267
AB - A new generalization of realcompactness based on ultrafilters of regular $F_{\sigma }$-subsets is introduced. Its relationship with realcompactness, almost realcompactness, almost* realcompactness, c-realcompactness is examined. Some of the properties of the newly introduced space is studied as well.
LA - eng
KW - regular $F_{\sigma }$-subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact; regular -subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact
UR - http://eudml.org/doc/246457
ER -

References

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  2. Bhattacharya D., Bhaumik R.N., Regular G -delta embeddings, Far East J. Math. Sci. (1997), Special Volume, Part II, 167–179. MR1605437
  3. Blair R.L., 10.4153/CJM-1976-068-9, Canad. J. Math. 28 (1976), 673–690. Zbl0359.54009MR0420542DOI10.4153/CJM-1976-068-9
  4. Dykes N., 10.2140/pjm.1970.33.571, Pacific J. Math. 33 (1970), 571–581. Zbl0197.19201MR0276928DOI10.2140/pjm.1970.33.571
  5. Frolík Z., A generalization of realcompact spaces, Czechoslovak Math. J. 13 (1963), 127–138. Zbl0112.37603MR0155289
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  7. Gillman L., Jerison M., Rings of Continuous Functions, University Series in Higher Math. Van Nostrand, Princeton, New Jersey, 1960. Zbl0327.46040MR0116199
  8. Hardy K., Woods R.G., 10.2140/pjm.1972.43.647, Pacific J. Math. 43 (1972), 647–656. Zbl0228.54019MR0365497DOI10.2140/pjm.1972.43.647
  9. Hewitt E., 10.1090/S0002-9947-1948-0026239-9, Trans. Amer. Math. Soc. 64 (1948), 54–99. Zbl0432.03030MR0026239DOI10.1090/S0002-9947-1948-0026239-9
  10. Horne J.G., Countable paracompactness and cb spaces, Notices Amer. Math. Soc. 6 (1959), 629–636. 
  11. Mack J.E., 10.1090/S0002-9947-1970-0259856-3, Trans. Amer. Math. Soc. 148 (1970), 265–272. Zbl0209.26904MR0259856DOI10.1090/S0002-9947-1970-0259856-3
  12. Mack J.E., Johnson D.G., 10.2140/pjm.1967.20.231, Pacific J. Math. 20 (1967), 231–243. MR0211268DOI10.2140/pjm.1967.20.231
  13. Mysior A., A union of realcompact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), no. 3–4, 169–172. Zbl0469.54011MR0638760
  14. Porter J., Woods R.G., Extensions and Absolutes of Hausdorff Spaces, Springer, New York, Heidelberg, Berlin, 1938. Zbl0652.54016MR0918341
  15. Schommer J., Swardson M.A., Almost* realcompactness, Comment. Math. Univ. Carolin. 42 (2001), no. 2, 385–394. MR1832157
  16. van der Slot J., Some properties related to compactness, Mathematical Centre Tracts, 19, Mathematisch Centrum, Amsterdam, 1968. Zbl0182.56204MR0247607

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