Continuous Selections for Set-Valued Mappings
نویسندگان
چکیده
منابع مشابه
Σ-products and selections of set-valued mappings
Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , 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.
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A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...
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We consider set valued mappings de ned on a linear normed space with convex closed images in IRn Our aim is to construct selections which are Hadamard directionally di erentiable using some approximation of the mul tifunction The constructions suggested assume existence of a cone approxima tion given by a certain derivative of the mapping The rst one makes use of the properties of Steiner point...
متن کاملDiierentiable Selections of Set-valued Mappings and Asymptotic Behaviour of Random Sets in Innnite Dimensions
We consider set-valued mappings acting between two linear normed spaces and having convex closed images. Our aim is to construct selections with directional diierentiability properties up to the second order, using certain tangential approximations of the mapping. The constructions preserve measurability and lead to a directionally diierentiable Castaing representation of measurable multifuncti...
متن کاملThe Whitney Extension Problem and Lipschitz Selections of Set-valued Mappings in Jet-spaces
We study a variant of the Whitney extension problem (1934) for the space Ck,ω(Rn). We identify Ck,ω(Rn) with a space of Lipschitzmappings from Rn into the space Pk × Rn of polynomial fields on Rn equipped with a certain metric. This identification allows us to reformulate the Whitney problem for Ck,ω(Rn) as a Lipschitz selection problem for set-valued mappings into a certain family of subsets o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1480