Finite-dimensional maps and dendrites with dense sets of end points

Hisao Kato; Eiichi Matsuhashi

Colloquium Mathematicae, Tome 106 (2006), p. 83-91 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $C (X, I^{p + 2 k + 1 - i})$ such that the diagonal product $f \times g : X \to Y \times I^{p + 2 k + 1 - i}$ is an (i+1)-to-1 map is a dense $G_{δ}$ -subset of $C (X, I^{p + 2 k + 1 - i})$ . 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 $C (X, \prod_{j = 1}^{k} D_{j} \times I^{p + 1 - i})$ such that $f \times h : X \to Y \times (\prod_{j = 1}^{k} D_{j} \times I^{p + 1 - i})$ is (i+1)-to-1 is a dense $G_{δ}$ -subset of $C (X, \prod_{j = 1}^{k} D_{j} \times I^{p + 1 - i})$ for each 0 ≤ i ≤ p.

Publié le : 2006-01-01

Zbl 1096.54015

EUDML-ID : urn:eudml:doc:283627

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     title = {Finite-dimensional maps and dendrites with dense sets of end points},
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     year = {2006},
     pages = {83-91},
     zbl = {1096.54015},
     language = {en},
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Hisao Kato; Eiichi Matsuhashi. Finite-dimensional maps and dendrites with dense sets of end points. Colloquium Mathematicae, Tome 106 (2006) pp. 83-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-7/