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Continuous selections, G δ -subsets of Banach spaces and usco mappings

Valentin G. Gutev — 1994

Commentationes Mathematicae Universitatis Carolinae

Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) G δ -subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.

Factorizations of set-valued mappings with separable range

Valentin G. Gutev — 1996

Commentationes Mathematicae Universitatis Carolinae

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.

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