# 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

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topLaguna, 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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