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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-6,
author = {Takahisa Miyata and \v Ziga Virk},
title = {Dimension-raising maps in a large scale},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {83-97},
zbl = {1288.54025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-6}
}
Takahisa Miyata; Žiga Virk. Dimension-raising maps in a large scale. Fundamenta Mathematicae, Tome 220 (2013) pp. 83-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-6/