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Continuous selection theorems

Michał Kisielewicz (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.

Continuous selections and approximations in α-convex metric spaces

A. Kowalska (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

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

Valentin G. Gutev (1994)

Commentationes Mathematicae Universitatis Carolinae

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.

Continuous Selections in α-Convex Metric Spaces

F. S. De Blasi, G. Pianigiani (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

For a space Z , we denote by ( Z ) , 𝒦 ( Z ) and 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality 2 of Z , respectively, with their Vietoris topology. For spaces X and E , C p ( X , E ) is the space of continuous functions from X to E with its pointwise convergence topology. We analyze in this article when ( Z ) , 𝒦 ( Z ) and 2 ( Z ) have continuous selections for a space Z of the form C p ( X , E ) , where X is zero-dimensional and E is a strongly zero-dimensional metrizable space. We prove that C p ( X , E ) is weakly orderable if and...

Continuous version of the Choquet integral representation theorem

Piotr Puchała (2005)

Studia Mathematica

Let E be a locally convex topological Hausdorff space, K a nonempty compact convex subset of E, μ a regular Borel probability measure on E and γ > 0. We say that the measure μ γ-represents a point x ∈ K if s u p | | f | | 1 | f ( x ) - K f d μ | < γ for any f ∈ E*. In this paper a continuous version of the Choquet theorem is proved, namely, if P is a continuous multivalued mapping from a metric space T into the space of nonempty, bounded convex subsets of a Banach space X, then there exists a weak* continuous family ( μ t ) of regular Borel...

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