Abstract: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 Dieudonn\'e completeness and Lindel\"of property in similar formulations.
Keywords: set-valued mapping, selection, realcompact, Dieudonn\'e complete, Lindel\"of, $\Cal B$-fixed, local intersection property, open lower sections
AMS Subject Classification: 54C60, 54C65, 54D20, 54D60