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

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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 $(2^{ℝ^2}, d_S)$ 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

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