Displaying similar documents to “On δ -continuous selections of small multifunctions and covering properties”

Selections and representations of multifunctions in paracompact spaces

Alberto Bressan, Giovanni Colombo (1992)

Studia Mathematica

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Let (X,T) be a paracompact space, Y a complete metric space, F : X → 2 Y a lower semicontinuous multifunction with nonempty closed values. We prove that if T + is a (stronger than T) topology on X satisfying a compatibility property, then F admits a T + -continuous selection. If Y is separable, then there exists a sequence ( f n ) of T + -continuous selections such that F ( x ) = f n ( x ) ; n ≥ 1 ¯ for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets...

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.

A generalization of the Schauder fixed point theorem via multivalued contractions

Paolo Cubiotti, Beatrice Di Bella (2001)

Commentationes Mathematicae Universitatis Carolinae

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We establish a fixed point theorem for a continuous function f : X → E , where E is a Banach space and X ⊆ E . Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.