PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Dimension-raising maps in a large scale

Volume 223 / 2013

Takahisa Miyata, Žiga Virk Fundamenta Mathematicae 223 (2013), 83-97 MSC: Primary 54F45; Secondary 54E35. DOI: 10.4064/fm223-1-6

Abstract

Hurewicz's dimension-raising theorem states that $\dim Y \leq \dim X + n$ for every $n$-to-$1$ map $f: X\rightarrow Y$. 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 $\dim X \leq n$ 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.

Authors

  • Takahisa MiyataDepartment of Mathematics and Informatics
    Graduate School of Human Development
    and Environment
    Kobe University
    Kobe, 657-8501 Japan
    e-mail
  • Žiga VirkFaculty of Mathematics and Physics
    University of Ljubljana
    Jadranska 21
    Ljubljana, 1000 Slovenia
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image