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1
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Whitney Preserving Maps onto Dendrites

100%
Matsuhashi E.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2012
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tom 60
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nr 2
155-163
EN
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.
2
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On Applications of Bing-Krasinkiewicz-Lelek Maps

100%
Matsuhashi E.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2007
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tom 55
|
nr 3
219-228
EN
We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.
3
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Krasinkiewicz maps from compacta to polyhedra

100%
Matsuhashi E.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2006
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tom 54
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nr 2
137-146
EN
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 $G_δ$-subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.
4
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Finite-dimensional maps and dendrites with dense sets of end points

64%
Kato H., Matsuhashi E.
Colloquium Mathematicum
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2006
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tom 106
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nr 1
83-91
EN
The first author has recently proved that if f: X → Y is a k-dimensional map between compacta and Y is p-dimensional (0 ≤ k, p < ∞), then for each 0 ≤ i ≤ p + k, the set of maps g in the space $C(X,I^{p+2k+1-i})$ such that the diagonal product $f×g: X → Y×I^{p+2k+1-i}$ is an (i+1)-to-1 map is a dense $G_{δ}$-subset of $C(X,I^{p+2k+1-i})$. In this paper, we prove that if f: X → Y is as above and $D_{j}$ (j = 1,..., k) are superdendrites, then the set of maps h in $C(X,∏_{j=1}^{k} D_{j}×I^{p+1-i})$ such that $f×h: X → Y×(∏_{j=1}^{k} D_{j}×I^{p+1-i})$ is (i+1)-to-1 is a dense $G_{δ}$-subset of $C(X,∏_{j=1}^{k} D_{j}×I^{p+1-i})$ for each 0 ≤ i ≤ p.
5
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On Surjective Bing Maps

64%
Kato H., Matsuhashi E.
Bulletin of the Polish Academy of Sciences. Mathematics
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2004
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tom 52
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nr 3
329-333
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 $G_δ$-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.
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