Fernández Laguna, Víctor and Morón, Manuel A. and Nhu, Nguyen Tho and Rodríguez Sanjurjo, José Manuel
(1993)
*Movability and limits of polyhedra.*
Fundamenta Mathematicae, 143
(3).
pp. 191-201.
ISSN 0016-2736

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## Abstract

We define a metric d(S), called the shape metric, on the hyperspace 2X 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 (2R2, d(S)) is separable. On the other hand, we give an example showing that 2R2 is not separable in the fundamental metric introduced by Borsuk.

Item Type: | Article |
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Uncontrolled Keywords: | Shape metric; polyhedra; metric space |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15543 |

References: | S. A. Bogatyĭ, Approximative and fundamental retracts, Mat. Sb. 93 (135) (1974), 90–102. K. Borsuk, On some metrization of the hyperspace of compact sets, Fund. Math. 41 (1954), 168–202. Theory of Shape, Monografie Mat. 59, Polish Scientific Publishers, Warszawa, 1975. On a metrization of the hyperspace of a metric space, Fund. Math. 94 (1977), 191–207. L. Boxer, Hyperspaces where convergence to a calm limit implies eventual shape equivalence, ibid. 115 (1983), 213–222. L. Boxer and R. B. Sher, Borsuk’s fundamental metric and shape domination, Bull. Acad. Polon. Sci. 26 (1978), 849–853. Z. Čerin, Cp-movably regular convergences, Fund. Math. 119 (1983), 249–268. C-E-movable and (C,D)-E-tame compacta, Houston J. Math. 9 (1983), 9–27. Z. Čerin and P. Šostak, Some remarks on Borsuk’s fundamental metric, in: Á. Császár (ed.), Proc. Colloq. Topology, Budapest, 1978, Colloq. Math. Soc. János Bolyai 23, North-Holland, Amsterdam, 1980, 233–252. M. H. Clapp, On a generalization of absolute neighbourhood retracts, Fund. Math. 70 (1971), 117–130. J. Dydak and J. Segal, Theory of Shape: An Introduction, Lecture Notes in Math. 688, Springer, Berlin, 1978. S. Godlewski, On shape of solenoids, Bull. Acad. Polon. Sci. 17 (1969), 623–627. L. S. Husch, Intersections of ANR’s, Fund. Math. 104 (1979), 21–26. V. Klee, Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30–45. S. Mardešić and J. Segal, Shape Theory, North-Holland, 1982. S. B. Nadler, Hyperspaces of Sets, Dekker, New York, 1978. H. Noguchi, A generalization of absolute neighbourhood retracts, Kodai Math.Sem. Rep. 1 (1953), 20–22. S. Spież, Movability and uniform movability, Bull. Acad. Polon. Sci. 22 (1974), 43–45. J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer, Berlin, 1975. |

Deposited On: | 08 Jun 2012 09:03 |

Last Modified: | 06 Feb 2014 10:26 |

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