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

Similarity:

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

Similarity:

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

Similarity:

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.

Relative normality and product spaces

Takao Hoshina, Ryoken Sokei (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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,...