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1993 | 143 | 3 | 191-201
Tytuł artykułu

Movability and limits of polyhedra

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
143
Numer
3
Strony
191-201
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-02-18
poprawiono
1992-11-19
poprawiono
1993-02-17
Twórcy
autor
  • Departamento de Matematica Fundamental, Facultad de Ciencias, U.N.E.D., 28040 Madrid, Spain
autor
  • 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
Bibliografia
  • [1] S. A. Bogatyĭ, Approximative and fundamental retracts, Mat. Sb. 93 (135) (1974), 90-102.
  • [2] K. Borsuk, On some metrization of the hyperspace of compact sets, Fund. Math. 41 (1954), 168-202.
  • [3] K. Borsuk, Theory of Shape, Monografie Mat. 59, Polish Scientific Publishers, Warszawa, 1975.
  • [4] K. Borsuk, On a metrization of the hyperspace of a metric space, Fund. Math. 94 (1977), 191-207.
  • [5] L. Boxer, Hyperspaces where convergence to a calm limit implies eventual shape equivalence, ibid. 115 (1983), 213-222.
  • [6] L. Boxer and R. B. Sher, Borsuk's fundamental metric and shape domination, Bull. Acad. Polon. Sci. 26 (1978), 849-853.
  • [7] Z. Čerin, $C_p$-movably regular convergences, Fund. Math. 119 (1983), 249-268.
  • [8] Z. Čerin, C-E-movable and (C,D)-E-tame compacta, Houston J. Math. 9 (1983), 9-27.
  • [9] 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.
  • [10] M. H. Clapp, On a generalization of absolute neighbourhood retracts, Fund. Math. 70 (1971), 117-130.
  • [11] J. Dydak and J. Segal, Theory of Shape : An Introduction, Lecture Notes in Math. 688, Springer, Berlin, 1978.
  • [12] S. Godlewski, On shape of solenoids, Bull. Acad. Polon. Sci. 17 (1969), 623-627.
  • [13] L. S. Husch, Intersections of ANR's, Fund. Math. 104 (1979), 21-26.
  • [14] V. Klee, Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30-45.
  • [15] S. Mardešić and J. Segal, Shape Theory, North-Holland, 1982.
  • [16] S. B. Nadler, Hyperspaces of Sets, Dekker, New York, 1978.
  • [17] H. Noguchi, A generalization of absolute neighbourhood retracts, Kodai Math. Sem. Rep. 1 (1953), 20-22.
  • [18] S. Spież, Movability and uniform movability, Bull. Acad. Polon. Sci. 22 (1974), 43-45.
  • [19] J. H. Wells and L. R. Williams, Embeddings and Extensions in Analysis, Springer, Berlin, 1975.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv143i3p191bwm
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