Movability and limits of polyhedra

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

ArticleOriginal scientific text

Title

Movability and limits of polyhedra

Authors ¹, ², ³, ⁴

Affiliations

Departamento de Matematica Fundamental, Facultad de Ciencias, U.N.E.D., 28040 Madrid, Spain
Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam
Departamento de Matematicas, E.T.S.I. de Montes, Universidad Politecnica, 28040 Madrid, Spain
Departamento de Geometria Y Topologia, Facultad de Matematicas, Universidad Complutense, 28040 Madrid, Spain

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}, d_{S})

is separable. On the other hand, we give an example showing that

2^{ℝ}^2}

is not separable in the fundamental metric introduced by Borsuk.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14331.pdf

Title

Movability and limits of polyhedra

Affiliations

Abstract

Bibliography

Additional information