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Original scientific paper

Bi-Lipschitz maps and the category of approximate resolutions

Takahisa Miyata
Tadashi Watanabe

Fulltext: english, pdf (948 KB) pages 129-155 downloads: 45* cite
APA 6th Edition
Miyata, T. & Watanabe, T. (2003). Bi-Lipschitz maps and the category of approximate resolutions. Glasnik matematički, 38 (1), 129-155. Retrieved from https://hrcak.srce.hr/1340
MLA 8th Edition
Miyata, Takahisa and Tadashi Watanabe. "Bi-Lipschitz maps and the category of approximate resolutions." Glasnik matematički, vol. 38, no. 1, 2003, pp. 129-155. https://hrcak.srce.hr/1340. Accessed 3 Dec. 2021.
Chicago 17th Edition
Miyata, Takahisa and Tadashi Watanabe. "Bi-Lipschitz maps and the category of approximate resolutions." Glasnik matematički 38, no. 1 (2003): 129-155. https://hrcak.srce.hr/1340
Harvard
Miyata, T., and Watanabe, T. (2003). 'Bi-Lipschitz maps and the category of approximate resolutions', Glasnik matematički, 38(1), pp. 129-155. Available at: https://hrcak.srce.hr/1340 (Accessed 03 December 2021)
Vancouver
Miyata T, Watanabe T. Bi-Lipschitz maps and the category of approximate resolutions. Glasnik matematički [Internet]. 2003 [cited 2021 December 03];38(1):129-155. Available from: https://hrcak.srce.hr/1340
IEEE
T. Miyata and T. Watanabe, "Bi-Lipschitz maps and the category of approximate resolutions", Glasnik matematički, vol.38, no. 1, pp. 129-155, 2003. [Online]. Available: https://hrcak.srce.hr/1340. [Accessed: 03 December 2021]

Abstracts
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

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