Valentin G. Gutev (1994)
Commentationes Mathematicae Universitatis Carolinae
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Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) -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.
Ivailo Shishkov (2000)
Commentationes Mathematicae Universitatis Carolinae
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Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.
Valentin G. Gutev (1996)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
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.