Continuous selections of the metric projection for 1-Chebyshev spaces
نویسندگان
چکیده
منابع مشابه
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.
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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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The articles [9], [5], [11], [1], [10], [6], [3], [4], [2], [8], [12], and [7] provide the notation and terminology for this paper. We introduce metric structures which are extensions of 1-sorted structure and are systems 〈 a carrier, a distance 〉, where the carrier is a set and the distance is a function from [: the carrier, the carrier :] into R. One can check that there exists a metric struc...
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If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S ∪ {1} is closed in G, then S is called a suitable set for G. We apply Michael’s selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris [8] on the existence of suitable sets in locally compact groups. Our approach uses only elementar...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1979
ISSN: 0021-9045
DOI: 10.1016/0021-9045(79)90131-x