Dimension-raising maps in a large scale

• Autorzy: Takahisa Miyata , Žiga Virk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 1
• Strony: 83-97

Daty

wydano

2013

Twórcy

autor

Takahisa Miyata

• Department of Mathematics and Informatics, Graduate School of Human Development, and Environment, Kobe University, Kobe, 657-8501 Japan

autor

Žiga Virk

• Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, Ljubljana, 1000 Slovenia

Identyfikatory

DOI

10.4064/fm223-1-6