Dimension-raising maps in a large scale

@article{TakahisaMiyata2013,
abstract = {Hurewicz's dimension-raising theorem states that dim Y ≤ dim X + n for every n-to-1 map f: X → Y. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a dimension-raising type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension. It is also well-known (Hurewicz's finite-to-one mapping theorem) that dim X ≤ n if and only if there exists an (n+1)-to-1 map from a 0-dimensional space onto X. We formulate a finite-to-one mapping type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension.},
author = {Takahisa Miyata, Žiga Virk},
journal = {Fundamenta Mathematicae},
keywords = {asymptotic dimension; asymptotic Assouad-Nagata dimension; dimension-raising map; finite-to-one map; coarse category},
language = {eng},
number = {1},
pages = {83-97},
title = {Dimension-raising maps in a large scale},
url = {http://eudml.org/doc/282731},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Takahisa Miyata
AU - Žiga Virk
TI - Dimension-raising maps in a large scale
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 1
SP - 83
EP - 97
AB - Hurewicz's dimension-raising theorem states that dim Y ≤ dim X + n for every n-to-1 map f: X → Y. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a dimension-raising type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension. It is also well-known (Hurewicz's finite-to-one mapping theorem) that dim X ≤ n if and only if there exists an (n+1)-to-1 map from a 0-dimensional space onto X. We formulate a finite-to-one mapping type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension.
LA - eng
KW - asymptotic dimension; asymptotic Assouad-Nagata dimension; dimension-raising map; finite-to-one map; coarse category
UR - http://eudml.org/doc/282731
ER -