On surjective bing maps

• Autorzy: Kato H. , Matsuhashi E.
• 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.

Słowa kluczowe

EN

hereditarily indecomposable continuum; Bing compactum; Menger manifold; 0-dimensional map

PL

kompakt Binga; odwzorowanie Binga; rozmaitość Mengera; odwzorowanie 0-wymiarowe

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 329--333
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kato H.

• Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan

autor

Matsuhashi E.

• 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.