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Approximate resolutions and the fractal category

Takahisa Miyata
Tadashi Watanabe

Puni tekst: engleski, pdf (583 KB) str. 377-393 preuzimanja: 45* citiraj
APA 6th Edition
Miyata, T. i Watanabe, T. (2003). Approximate resolutions and the fractal category. Glasnik matematički, 38 (2), 377-393. Preuzeto s https://hrcak.srce.hr/1328
MLA 8th Edition
Miyata, Takahisa i Tadashi Watanabe. "Approximate resolutions and the fractal category." Glasnik matematički, vol. 38, br. 2, 2003, str. 377-393. https://hrcak.srce.hr/1328. Citirano 22.10.2021.
Chicago 17th Edition
Miyata, Takahisa i Tadashi Watanabe. "Approximate resolutions and the fractal category." Glasnik matematički 38, br. 2 (2003): 377-393. https://hrcak.srce.hr/1328
Harvard
Miyata, T., i Watanabe, T. (2003). 'Approximate resolutions and the fractal category', Glasnik matematički, 38(2), str. 377-393. Preuzeto s: https://hrcak.srce.hr/1328 (Datum pristupa: 22.10.2021.)
Vancouver
Miyata T, Watanabe T. Approximate resolutions and the fractal category. Glasnik matematički [Internet]. 2003 [pristupljeno 22.10.2021.];38(2):377-393. Dostupno na: https://hrcak.srce.hr/1328
IEEE
T. Miyata i T. Watanabe, "Approximate resolutions and the fractal category", Glasnik matematički, vol.38, br. 2, str. 377-393, 2003. [Online]. Dostupno na: https://hrcak.srce.hr/1328. [Citirano: 22.10.2021.]

Sažetak
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.

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

Hrčak ID: 1328

URI
https://hrcak.srce.hr/1328

Posjeta: 215 *