Movability and limits of polyhedra

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

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 3, page 191-201
  • ISSN: 0016-2736

Abstract

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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 .

How to cite

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Laguna, V., et al. "Movability and limits of polyhedra." Fundamenta Mathematicae 143.3 (1993): 191-201. <http://eudml.org/doc/212003>.

@article{Laguna1993,
abstract = {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)$ is separable. On the other hand, we give an example showing that $2ℝ2$ is not separable in the fundamental metric introduced by Borsuk.$},
author = {Laguna, V., Moron, M., Nguyen, Nhu, Sanjurjo, J.},
journal = {Fundamenta Mathematicae},
keywords = {movability; polyhedron; shape metric; fundamental metric},
language = {eng},
number = {3},
pages = {191-201},
title = {Movability and limits of polyhedra},
url = {http://eudml.org/doc/212003},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Laguna, V.
AU - Moron, M.
AU - Nguyen, Nhu
AU - Sanjurjo, J.
TI - Movability and limits of polyhedra
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 3
SP - 191
EP - 201
AB - 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)$ is separable. On the other hand, we give an example showing that $2ℝ2$ is not separable in the fundamental metric introduced by Borsuk.$
LA - eng
KW - movability; polyhedron; shape metric; fundamental metric
UR - http://eudml.org/doc/212003
ER -

References

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