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

Hisao Kato, and Eiichi Matsuhashi. "Finite-dimensional maps and dendrites with dense sets of end points." Colloquium Mathematicae 106.1 (2006): 83-91. <http://eudml.org/doc/283627>.

@article{HisaoKato2006,
abstract = {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.},
author = {Hisao Kato, Eiichi Matsuhashi},
journal = {Colloquium Mathematicae},
keywords = {compact metrizable space; dimension; finite-dimensional map; finite-to-one map; embedding; superdendrite; -set; -set; map parallel to a superdendrite},
language = {eng},
number = {1},
pages = {83-91},
title = {Finite-dimensional maps and dendrites with dense sets of end points},
url = {http://eudml.org/doc/283627},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Hisao Kato
AU - Eiichi Matsuhashi
TI - Finite-dimensional maps and dendrites with dense sets of end points
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 83
EP - 91
AB - 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.
LA - eng
KW - compact metrizable space; dimension; finite-dimensional map; finite-to-one map; embedding; superdendrite; -set; -set; map parallel to a superdendrite
UR - http://eudml.org/doc/283627
ER -