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Original scientific paper
https://doi.org/10.3336/gm.47.2.17

Property A and asymptotic dimension

Matija Cencelj ; Pedagoška fakulteta, Univerza v Ljubljani, Kardeljeva pl. 16, SI-1111 Ljubljana, Slovenija
Jerzy Dydak   ORCID icon orcid.org/0000-0003-3302-9881 ; University of Tennessee, Knoxville, TN 37996, USA
Aleš Vavpetič ; Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska ulica 19, SI-1111 Ljubljana, Slovenija

Fulltext: english, pdf (91 KB) pages 441-444 downloads: 222* cite
APA 6th Edition
Cencelj, M., Dydak, J. & Vavpetič, A. (2012). Property A and asymptotic dimension. Glasnik matematički, 47 (2), 441-444. https://doi.org/10.3336/gm.47.2.17
MLA 8th Edition
Cencelj, Matija, et al. "Property A and asymptotic dimension." Glasnik matematički, vol. 47, no. 2, 2012, pp. 441-444. https://doi.org/10.3336/gm.47.2.17. Accessed 5 Dec. 2021.
Chicago 17th Edition
Cencelj, Matija, Jerzy Dydak and Aleš Vavpetič. "Property A and asymptotic dimension." Glasnik matematički 47, no. 2 (2012): 441-444. https://doi.org/10.3336/gm.47.2.17
Harvard
Cencelj, M., Dydak, J., and Vavpetič, A. (2012). 'Property A and asymptotic dimension', Glasnik matematički, 47(2), pp. 441-444. https://doi.org/10.3336/gm.47.2.17
Vancouver
Cencelj M, Dydak J, Vavpetič A. Property A and asymptotic dimension. Glasnik matematički [Internet]. 2012 [cited 2021 December 05];47(2):441-444. https://doi.org/10.3336/gm.47.2.17
IEEE
M. Cencelj, J. Dydak and A. Vavpetič, "Property A and asymptotic dimension", Glasnik matematički, vol.47, no. 2, pp. 441-444, 2012. [Online]. https://doi.org/10.3336/gm.47.2.17

Abstracts
The purpose of this note is to characterize the asymptotic dimension asdim(X) of metric spaces X in terms similar to Property A of Guoliang Yu. We prove that for a metric space (X,d) and n≥ 0 the following conditions are equivalent:

asdim(X,d)≤ n.
For each R,ε > 0 there is S > 0 and finite non-empty subsets Ax⊂ B(x,S)× N, x X, such that |AxΔ Ay| / |Ax∩ Ay| < ε if d(x,y) < R and the projection of Ax onto X contains at most n+1 elements for all x X.
For each R > 0 there is S > 0 and finite non-empty subsets Ax⊂ B(x,S)× N, x X, such that |AxΔ Ay| / |Ax∩ Ay| < 1/(n+1) if d(x,y) < R and the projection of Ax onto X contains at most n+1 elements for all x X.

Keywords
Asymptotic dimension; Property A

Hrčak ID: 93960

URI
https://hrcak.srce.hr/93960

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