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Keywords:
set-valued mapping; selection; realcompact; Dieudonné complete; Lindelöf; $\Cal B$-fixed; local intersection property; open lower sections
set-valued mapping; selection; realcompact; Dieudonné complete; Lindelöf; $\Cal B$-fixed; local intersection property; open lower sections
Summary:
Blum and Swaminathan [Pacific J. Math. 93 (1981), 251--260] introduced the notion of $\Cal B$-fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.
References:
[1] Aló R.A., Shapiro H.L.: Normal Topological Spaces. Cambridge University Press, New York-London, 1974. MR 0390985
[2] Blum I., Swaminathan S.: Continuous selections and realcompactness. Pacific J. Math. 93 (1981), 251-260. MR 0623561 | Zbl 0457.54012
[3] De Marco G., Wilson R.G.: Realcompactness and partitions of unity. Proc. Amer. Math. Soc. 30 (1971), 189-194. MR 0281155
[4] Engelking R.: General Topology. Heldermann Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[5] Gillman L., Jerison M.: Rings of Continuous Functions. D. Van Nostrand Co., Inc., Princeton, NJ.-Toronto-London-New York, 1960. MR 0116199 | Zbl 0327.46040
[6] Michael E.: Continuous selection I. Ann. Math. 63 (1956), 361-382. MR 0077107
[7] Michael E.: A theorem on semi-continuous set-valued functions. Duke Math. J. 26 (1959), 647-651. MR 0109343 | Zbl 0151.30805
[8] Nedev S.: Selection and factorization theorems for set-valued mappings. Serdica 6 (1980), 291-317. MR 0644284 | Zbl 0492.54006
[9] Repovš D., Semenov P.V.: Continuous selections of multivalued mappings. Kluwer Acad. Publ., Dordrecht, 1998. MR 1659914
[10] Tamano H.: On compactifications. J. Math. Kyoto Univ. 1 (1962), 162-193. MR 0142096 | Zbl 0106.15601
[11] Wiscamb M.R.: The discrete countable chain condition. Proc. Amer. Math. Soc. 23 (1969), 608-612. MR 0248744 | Zbl 0184.26304
[12] Wu X., Shen S.: A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications. J. Math. Anal. Appl. 197 (1996), 61-74. MR 1371276 | Zbl 0852.54019
[13] Yannelis N.C., Prabhakar N.D.: Existence of maximal elements and equilibria in linear topological spaces. J. Math. Econom. 12 (1983), 233-245. MR 0743037 | Zbl 0536.90019
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