Displaying similar documents to “Continuous selections, G δ -subsets of Banach spaces and usco mappings”

Σ -products and selections of set-valued mappings

Ivailo Shishkov (2001)

Commentationes Mathematicae Universitatis Carolinae

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Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 Y , where X is a Σ -product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

On a selection theorem of Blum and Swaminathan

Takamitsu Yamauchi (2004)

Commentationes Mathematicae Universitatis Carolinae

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Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of 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.

On δ -continuous selections of small multifunctions and covering properties

Alessandro Fedeli, Jan Pelant (1991)

Commentationes Mathematicae Universitatis Carolinae

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The spaces for which each δ -continuous function can be extended to a 2 δ -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.