Movability and limits of polyhedra

Laguna, V.; Moron, M.; Nguyen, Nhu; Sanjurjo, J.

Laguna, V. ; Moron, M. ; Nguyen, Nhu ; Sanjurjo, J.

Fundamenta Mathematicae, Tome 142 (1993), p. 191-201 / Harvested from The Polish Digital Mathematics Library

Résumé

We define a metric $d_{S}$ , called the shape metric, on the hyperspace $2^{X}$ of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace $(2^{ℝ} 2$ , dS) $i s s e p a r a b l e . O n t h e o t h e r h a n d, w e g i v e a n e x a m p l e s h o w i n g t h a t$ 2ℝ2 $i s n o t s e p a r a b l e i n t h e f u n d a m e n t a l m e t r i c i n t r o d u c e d b y B o r s u k .$

Publié le : 1993-01-01

Zbl 0806.54016

EUDML-ID : urn:eudml:doc:212003

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     author = {V. Laguna and M. Moron and Nhu Nguyen and J. Sanjurjo},
     title = {Movability and limits of polyhedra},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {191-201},
     zbl = {0806.54016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p191bwm}
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Laguna, V.; Moron, M.; Nguyen, Nhu; Sanjurjo, J. Movability and limits of polyhedra. Fundamenta Mathematicae, Tome 142 (1993) pp. 191-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p191bwm/

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