Original scientific paper

Approximate resolutions and the fractal category

Takahisa Miyata
Tadashi Watanabe

Abstract

This paper concerns the theory of approximate resolutions and its application to fractal geometry. In this paper, we first characterize a surjective map f : X Y between compact metric spaces in terms of a property on any approximate map f : X Y where p : X X and q : Y Y are any choices of approximate resolutions of X and Y, respectively. Using this characterization, we construct a category whose objects are approximate sequences so that the box-counting dimension, which was defined for approximate resolutions by the authors, is invariant in this category. To define the morphisms of the category, we introduce an equivalence relation on approximate maps and define the morphisms as the equivalence classes.

Keywords

Approximate resolution; surjective map; box-counting dimension; category

Hrčak ID:

1328

URI

https://hrcak.srce.hr/1328

Publication date:

1.12.2003.

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