Trivial bundles of spaces of probability measures and countable-dimensionality

Valentin Gutev

Displaying similar documents to “Trivial bundles of spaces of probability measures and countable-dimensionality”

On a question of E.A. Michael

Vladimir V. Filippov (2004)

Commentationes Mathematicae Universitatis Carolinae

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A negative answer to a question of E.A. Michael is given: A convex $G_{δ}$ -subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y \to Y$ having closed convex values and no continuous selection.

Factorizations of set-valued mappings with separable range

Valentin G. Gutev (1996)

Commentationes Mathematicae Universitatis Carolinae

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Right factorizations for a class of l.s.cṁappings with separable metrizable range are constructed. Besides in the selection and dimension theories, these l.s.cḟactorizations are also successful in solving the problem of factorizing a class of u.s.cṁappings.

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.