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Isometries of spaces of compact or compact convex subsets of metric manifolds

✍ Scribed by P. M. Gruber; R. Tichy

Publisher
Springer Vienna
Year
1982
Tongue
English
Weight
450 KB
Volume
93
Category
Article
ISSN
0026-9255

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πŸ“œ SIMILAR VOLUMES

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Let Yd" be the space of compact subsets of E a, endowed with the Hausdorffmetric. It is shown that the isometries of ~ onto itself are the mappings generated by rigid motions of E a.

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In this paper, we prove that every isometry from a nonempty weakly compact convex set K into itself fixes a point in the Chebyshev center of K, provided K satisfies the hereditary fixed point property for isometries. In particular, all isometries from a nonempty bounded closed convex subset of a uni

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## Abstract Although classically every open subspace of a locally compact space is also locally compact, constructively this is not generally true. This paper provides a locally compact remetrization for an open set in a compact metric space and constructs a one‐point compactification. MSC: 54D45,