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Dimension-raising maps in a large scale

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Miyata T., Virk Ž.

Fundamenta Mathematicae

2013

tom 223

nr 1

83-97

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.

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1 Fundamenta Mathematicae

1 Miyata T.

1 Virk Ž.

1 2013

Wyniki wyszukiwania

Dimension-raising maps in a large scale