Displaying similar documents to “ Σ -products and selections of set-valued mappings”

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

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) 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.

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.

Relative normality and product spaces

Takao Hoshina, Ryoken Sokei (2003)

Commentationes Mathematicae Universitatis Carolinae

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Arhangel’skiĭ defines in [Topology Appl. 70 (1996), 87–99], as one of various notions on relative topological properties, strong normality of A in X for a subspace A of a topological space X , and shows that this is equivalent to normality of X A , where X A denotes the space obtained from X by making each point of X ∖ A isolated. In this paper we investigate for a space X , its subspace A and a space Y the normality of the product X A × Y in connection with the normality of ( X × Y ) ( A × Y ) . The cases for paracompactness,...

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...