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4 Bulletin of the Polish Academy of Sciences. Mathematics

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Whitney Preserving Maps onto Dendrites

Matsuhashi E.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 2

155--163

We prove the following results. (i) Let X be a continuum such that X contains a dense arc component and let D be a dendrite with a closed set of branch points. If f:X→D is a Whitney preserving map, then f is a homeomorphism. (ii) For each dendrite D′ with a dense set of branch points there exist a continuum X′ containing a dense arc component and a Whitney preserving map f′:X′→D′ such that f′ is not a homeomorphism.

On applications of Bing-Krasinkiewicz-Lelek maps

Matsuhashi E.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 3

219-228

We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.

Krasinkiewicz maps from compacta to polyhedra

Matsuhashi E.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 2

137-146

We prove that the set of all Krasinkiewicz maps from a compact metric space to a polyhedron (or a 1-dimensional locally connected continuum, or an n-dimensional Menger manifold, n ≥ 1) is a dense Gδ-subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.

On surjective bing maps

Kato H., Matsuhashi E.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

329-333

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.