Geodesic
On a selection theorem of Blum and Swaminathan
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 681-691

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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.
Classification : 54C60, 54C65, 54D20, 54D60
Keywords: set-valued mapping; selection; realcompact; Dieudonné complete; Lindelöf; $\Cal B$-fixed; local intersection property; open lower sections 
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Yamauchi, Takamitsu. On a selection theorem of Blum and Swaminathan. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 681-691. http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a8/