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On surjective bing maps

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In [7], M. Levin proved that the set of all Bing maps of a compact metric space to the unit interval is a dense G[delta]-subset of the space of all maps. In [6], J. Krasinkiewicz . independently proved that the set of all Bing maps of a compact metric space to an n-dimensional manifold (n is less than or equal to 1) is a dense G[delta]-subset of the space of maps. In [9], J. Song and E. D. Tymchatyn, solving some problems of J. Krasinkiewicz ([6]), proved that the set of all Bing maps of a compact metric space to a nondegenerate connected polyhedron is a dense G[delta]-subset of the space of maps. In this note, we investigate the existence of surjective Bing maps from continua to polyhedra.
Rocznik
Strony
329--333
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
  • Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan
  • Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan
Bibliografia
  • [1] M. Bestvina, Characterizing k-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 380 (1988).
  • [2] R. H. Bing, Higher-dimensional hereditarily indecomposable continua, Trans. Amer. Math. Soc. 71 (1951), 267-273.
  • [3] K. Borsuk, Theory of Retracts, PWN, Warszawa, 1967.
  • [4] M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 10 (1960), 478-483.
  • [5] R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann, 1995.
  • [6] J. Krasinkiewicz, On mappings with hereditarily indecomposable fibers, Bull. Polish Acad. Sci. Math. 44 (1996), 147-156.
  • [7] M. Levin, Bing maps and finite-dimensional maps, Fund. Math. 151 (1996), 47-52.
  • [8] S. B. Nadler Jr., Continuum Theory. An Introduction, Dekker, 1992.
  • [9] J. Song and E. D. Tymchatyn, Free spaces, Fund. Math. 163 (2000), 229-239.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0004-0034
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