On Surjective Bing Maps

Hisao Kato; Eiichi Matsuhashi

Bulletin of the Polish Academy of Sciences. Mathematics (2004)

  • Volume: 52, Issue: 3, page 329-333
  • ISSN: 0239-7269

Abstract

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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 δ -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 ≥ 1) is a dense G δ -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 δ -subset of the space of maps. In this note, we investigate the existence of surjective Bing maps from continua to polyhedra.

How to cite

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Hisao Kato, and Eiichi Matsuhashi. "On Surjective Bing Maps." Bulletin of the Polish Academy of Sciences. Mathematics 52.3 (2004): 329-333. <http://eudml.org/doc/280642>.

@article{HisaoKato2004,
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 $G_δ$-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 ≥ 1) is a dense $G_δ$-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 $G_δ$-subset of the space of maps. In this note, we investigate the existence of surjective Bing maps from continua to polyhedra.},
author = {Hisao Kato, Eiichi Matsuhashi},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {hereditarily indecomposable continuum; Bing compactum; Bing map; Menger manifold; 0-dimensional map},
language = {eng},
number = {3},
pages = {329-333},
title = {On Surjective Bing Maps},
url = {http://eudml.org/doc/280642},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Hisao Kato
AU - Eiichi Matsuhashi
TI - On Surjective Bing Maps
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 3
SP - 329
EP - 333
AB - In [7], M. Levin proved that the set of all Bing maps of a compact metric space to the unit interval is a dense $G_δ$-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 ≥ 1) is a dense $G_δ$-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 $G_δ$-subset of the space of maps. In this note, we investigate the existence of surjective Bing maps from continua to polyhedra.
LA - eng
KW - hereditarily indecomposable continuum; Bing compactum; Bing map; Menger manifold; 0-dimensional map
UR - http://eudml.org/doc/280642
ER -

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