Weak Chebyshev subspaces and continuous selections for the metric projection

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.

WEAK CHEBYSHEV SUBSPACES AND , 4 - SUBSPACES OF C [ a , b ]

In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus's characterization of Asubspaces of C[a, b]. As a consequence we obtain that if the metric projection PG from C[a, b] onto a finite-dimensional subspace G has a continuous selection and elements of G have no common zeros on (a, b), then G is an /4-subspace.

ε-weakly Chebyshev subspaces and quotient spaces

Continuous Selections and Approximations in Α-convex Metric Spaces

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.

Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

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...