On dimensionally restricted maps

H. Murat Tuncali, and Vesko Valov. "On dimensionally restricted maps." Fundamenta Mathematicae 175.1 (2002): 35-52. <http://eudml.org/doc/283094>.

@article{H2002,
abstract = {Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an $F_\{σ\}$-subset $A_\{k\}$ of X such that $dim A_\{k\} ≤ k$ and the restriction $f|(X∖A_\{k\})$ is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about extensional dimension is also established.},
author = {H. Murat Tuncali, Vesko Valov},
journal = {Fundamenta Mathematicae},
keywords = {finite-dimensional maps; extensional dimension; -spaces},
language = {eng},
number = {1},
pages = {35-52},
title = {On dimensionally restricted maps},
url = {http://eudml.org/doc/283094},
volume = {175},
year = {2002},
}

TY - JOUR
AU - H. Murat Tuncali
AU - Vesko Valov
TI - On dimensionally restricted maps
JO - Fundamenta Mathematicae
PY - 2002
VL - 175
IS - 1
SP - 35
EP - 52
AB - Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an $F_{σ}$-subset $A_{k}$ of X such that $dim A_{k} ≤ k$ and the restriction $f|(X∖A_{k})$ is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about extensional dimension is also established.
LA - eng
KW - finite-dimensional maps; extensional dimension; -spaces
UR - http://eudml.org/doc/283094
ER -