Department of Mathematics and Information Sciences,
Faculty of Education, Yamaguchi University,
Yamaguchi-City, 753-8513, JAPAN
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.
2000 Mathematics Subject Classification. 54C56, 28A80, 54F45, 54E40.
Key words and phrases. Approximate resolution, biLipschitz map, Lipschitz map, box-counting dimension, category.