Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
regular $F_{\sigma}$-subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact
regular $F_{\sigma}$-subsets; almost realcompactness; almost* realcompactness; r-weak cb; regular Oz; regular countably paracompact
Summary:
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.
References:
[1] Bhattacharya D., Bhaumik R.N.: Regular $G_{\delta}$-subsets and realcompact spaces. Bull. Calcutta Math. Soc. 87 (1995), 39–44. MR 1352064
[2] Bhattacharya D., Bhaumik R.N.: Regular $G$-delta embeddings. Far East J. Math. Sci. (1997), Special Volume, Part II, 167–179. MR 1605437
[3] Blair R.L.: Spaces in which special sets are z-embedded. Canad. J. Math. 28 (1976), 673–690. DOI 10.4153/CJM-1976-068-9 | MR 0420542 | Zbl 0359.54009
[4] Dykes N.: Generalizations of realcompact spaces. Pacific J. Math. 33 (1970), 571–581. DOI 10.2140/pjm.1970.33.571 | MR 0276928 | Zbl 0197.19201
[5] Frolík Z.: A generalization of realcompact spaces. Czechoslovak Math. J. 13 (1963), 127–138. MR 0155289 | Zbl 0112.37603
[6] Frolík Z.: Prime filters with CIP. Comment. Math. Univ. Carolin. 13 (1972), no. 3, 553–575. MR 0315648 | Zbl 0251.54001
[7] Gillman L., Jerison M.: Rings of Continuous Functions. University Series in Higher Math. Van Nostrand, Princeton, New Jersey, 1960. MR 0116199 | Zbl 0327.46040
[8] Hardy K., Woods R.G.: On c-realcompact spaces and locally bounded normal functions. Pacific J. Math. 43 (1972), 647–656. DOI 10.2140/pjm.1972.43.647 | MR 0365497 | Zbl 0228.54019
[9] Hewitt E.: Rings of real valued continuous functions. Trans. Amer. Math. Soc. 64 (1948), 54–99. DOI 10.1090/S0002-9947-1948-0026239-9 | MR 0026239 | Zbl 0432.03030
[10] Horne J.G.: Countable paracompactness and cb spaces. Notices Amer. Math. Soc. 6 (1959), 629–636.
[11] Mack J.E.: Countable paracompactness and weak normality properties. Trans. Amer. Math. Soc. 148 (1970), 265–272. DOI 10.1090/S0002-9947-1970-0259856-3 | MR 0259856 | Zbl 0209.26904
[12] Mack J.E., Johnson D.G.: The Dedekind completion of $C(X)$. Pacific J. Math. 20 (1967), 231–243. DOI 10.2140/pjm.1967.20.231 | MR 0211268
[13] Mysior A.: A union of realcompact spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), no. 3–4, 169–172. MR 0638760 | Zbl 0469.54011
[14] Porter J., Woods R.G.: Extensions and Absolutes of Hausdorff Spaces. Springer, New York, Heidelberg, Berlin, 1938. MR 0918341 | Zbl 0652.54016
[15] Schommer J., Swardson M.A.: Almost* realcompactness. Comment. Math. Univ. Carolin. 42 (2001), no. 2, 385–394. MR 1832157
[16] van der Slot J.: Some properties related to compactness. Mathematical Centre Tracts, 19, Mathematisch Centrum, Amsterdam, 1968. MR 0247607 | Zbl 0182.56204
Search
Partner of
