hrcak mascot   Srce   HID

Original scientific paper

Approximate resolutions and the fractal category

Takahisa Miyata
Tadashi Watanabe

Fulltext: english, pdf (583 KB) pages 377-393 downloads: 46* cite
APA 6th Edition
Miyata, T. & Watanabe, T. (2003). Approximate resolutions and the fractal category. Glasnik matematički, 38 (2), 377-393. Retrieved from https://hrcak.srce.hr/1328
MLA 8th Edition
Miyata, Takahisa and Tadashi Watanabe. "Approximate resolutions and the fractal category." Glasnik matematički, vol. 38, no. 2, 2003, pp. 377-393. https://hrcak.srce.hr/1328. Accessed 3 Dec. 2021.
Chicago 17th Edition
Miyata, Takahisa and Tadashi Watanabe. "Approximate resolutions and the fractal category." Glasnik matematički 38, no. 2 (2003): 377-393. https://hrcak.srce.hr/1328
Harvard
Miyata, T., and Watanabe, T. (2003). 'Approximate resolutions and the fractal category', Glasnik matematički, 38(2), pp. 377-393. Available at: https://hrcak.srce.hr/1328 (Accessed 03 December 2021)
Vancouver
Miyata T, Watanabe T. Approximate resolutions and the fractal category. Glasnik matematički [Internet]. 2003 [cited 2021 December 03];38(2):377-393. Available from: https://hrcak.srce.hr/1328
IEEE
T. Miyata and T. Watanabe, "Approximate resolutions and the fractal category", Glasnik matematički, vol.38, no. 2, pp. 377-393, 2003. [Online]. Available: https://hrcak.srce.hr/1328. [Accessed: 03 December 2021]

Abstracts
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

Visits: 222 *