Geodesic
Movability and limits of polyhedra
V. F. Laguna1 ; M. A. Moron2 ; Nguyen To Nhu3 ; J. M. R. Sanjurjo4
1 Departamento de Matematica Fundamental Facultad De Ciencias, U.N.E.D. 28040 Madrid, Spain
2 Departamento de Matematicas E.T.S.I. de Montes Universidad Politecnica 28040 Madrid, Spain
3 Institute of Mathematics P.O. Box 631 Bo Ho Hanoi, Vietnam
4 Departamento De Geometria y Topologia Facultad de Matematicas Universidad Complutense 28040 Madrid, Spain
Fundamenta Mathematicae, Tome 143 (1993) no. 3, pp. 191-201.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-143-3-191-201

V. F. Laguna 1 ; M. A. Moron 2 ; Nguyen To Nhu 3 ; J. M. R. Sanjurjo 4

1 Departamento de Matematica Fundamental Facultad De Ciencias, U.N.E.D. 28040 Madrid, Spain
2 Departamento de Matematicas E.T.S.I. de Montes Universidad Politecnica 28040 Madrid, Spain
3 Institute of Mathematics P.O. Box 631 Bo Ho Hanoi, Vietnam
4 Departamento De Geometria y Topologia Facultad de Matematicas Universidad Complutense 28040 Madrid, Spain 
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V. F. Laguna; M. A. Moron; Nguyen To Nhu; J. M. R. Sanjurjo. Movability and limits of polyhedra. Fundamenta Mathematicae, Tome 143 (1993) no. 3, pp. 191-201. doi : 10.4064/fm-143-3-191-201. http://geodesic.mathdoc.fr/articles/10.4064/fm-143-3-191-201/

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