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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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
83-97
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
- Department of Mathematics and Informatics, Graduate School of Human Development, and Environment, Kobe University, Kobe, 657-8501 Japan
autor
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, Ljubljana, 1000 Slovenia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-6