On Surjective Bing Maps

Volume 52 / 2004

Hisao Kato, Eiichi Matsuhashi Bulletin Polish Acad. Sci. Math. 52 (2004), 329-333 MSC: Primary 54F45, 54F15; Secondary 54C05, 54C35, 54C50. DOI: 10.4064/ba52-3-12

Abstract

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 ($n \ge 1$) 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.

Authors

  • Hisao KatoInstitute of Mathematics
    University of Tsukuba
    Ibaraki, 305-8571 Japan
    e-mail
  • Eiichi MatsuhashiInstitute of Mathematics
    University of Tsukuba
    Ibaraki, 305-8571 Japan
    e-mail

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