Original scientific paper

Bi-Lipschitz maps and the category of approximate resolutions

Takahisa Miyata
Tadashi Watanabe

Abstract

In this paper we consider biLipschitz maps between compact spaces with the metrics which are induced by given approximate resolutions. More precisely, we characterize biLipschitz maps in terms of conditions on any approximate resolutions of the maps. We then show that the box-counting dimension for approximate resolutions which was introduced earlier is invariant under approximate maps corresponding to biLipschitz maps. Moreover, we construct categories whose objects are approximate resolutions and in which the box-counting dimension is invariant.

Keywords

Approximate resolution; biLipschitz map; Lipschitz map; box-counting dimension; category

Hrčak ID:

1340

URI

https://hrcak.srce.hr/1340

Publication date:

1.6.2003.

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