On Surjective Bing Maps

Hisao Kato¹ ; Eiichi Matsuhashi¹

¹ Institute of Mathematics University of Tsukuba Ibaraki, 305-8571 Japan

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 329-333

Résumé

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.

Détail

DOI : 10.4064/ba52-3-12

Keywords: levin proved set bing maps compact metric space unit interval dense delta subset space maps krasinkiewicz independently proved set bing maps compact metric space n dimensional manifold dense delta subset space maps song tymchatyn solving problems krasinkiewicz proved set bing maps compact metric space nondegenerate connected polyhedron dense delta subset space maps note investigate existence surjective bing maps continua polyhedra