A remark on asymptotic dimension and digital dimension of finite metric spaces

V.Chatyrko; M.Zarichnyi

Relationships between the asymptotic dimension (in the sense of Gromov) of a proper metric space and the so-called digital dimension of its finite subspaces are established.

1. Bell G.C., Dranishnikov A.N., Keesling J.E. On a formula for the asymptotic dimension of free products, Fundam. Math. 183, No.1 (2004), 39--45.

2. Bell G., Dranishnikov A. On asymptotic dimension of groups, Algebr. Geom. Topol. 1 (2001), 57--71.

3. Bell G., Dranishnikov A. On asymptotic dimension of groups acting on trees, Geom. Dedicata 103 (2004) 89--101.

4. Dranishnikov A. Asymptotic topology, Russian Math. Surveys 55, No 6 (2000), 71--116.

5. Dranishnikov A. On asymptotic inductive dimension, JP J. Geom. Topol. 1 , no. 3 (2001), 239--247.

6. Dranishnikov A.N. On hypersphericity of manifolds with finite asymptotic dimension, Trans. Am. Math. Soc. 355, No.1 (2003), 155--167.

7. Dranishnikov A. Groups with a polynomial dimension growth, preprint.

8. Dranishnikov A. Dimension theory local and global, preprint.

9. Dranishnikov A., Keesling J.E., Uspenskij V.V. On the Higson corona of uniformly contractible spaces Topology, 37, No. 3 (1998), 791--803.

10. Dranishnikov A., Zarichnyi M. Universal spaces for asymptotic dimension, Topology Appl. 140, No.2-3 (2004), 203--225.

11. Gromov M. Asymptotic invariants of infinite groups. Geometric group theory, Vol. 2 (Sussex, 1991), 1--295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993.

12. Ostrand Ph. A. Dimension of metric spaces and Hilbert's problem $13$, Bull. Amer. Math. Soc. 71 (1965), 619--622.

	A remark on asymptotic dimension and digital dimension of finite metric spaces
Author	V.Chatyrko, M.Zarichnyi vitja@mai.liu.se, mzar@litech.lviv.ua University of Linköping, Ivan Franko National University of Lviv
Abstract	Relationships between the asymptotic dimension (in the sense of Gromov) of a proper metric space and the so-called digital dimension of its finite subspaces are established.
Keywords	asymptotic dimension, digital dimension, finite metric space
DOI	doi:10.30970/ms.27.1.100-104
Reference	1. Bell G.C., Dranishnikov A.N., Keesling J.E. On a formula for the asymptotic dimension of free products, Fundam. Math. 183, No.1 (2004), 39--45. 2. Bell G., Dranishnikov A. On asymptotic dimension of groups, Algebr. Geom. Topol. 1 (2001), 57--71. 3. Bell G., Dranishnikov A. On asymptotic dimension of groups acting on trees, Geom. Dedicata 103 (2004) 89--101. 4. Dranishnikov A. Asymptotic topology, Russian Math. Surveys 55, No 6 (2000), 71--116. 5. Dranishnikov A. On asymptotic inductive dimension, JP J. Geom. Topol. 1 , no. 3 (2001), 239--247. 6. Dranishnikov A.N. On hypersphericity of manifolds with finite asymptotic dimension, Trans. Am. Math. Soc. 355, No.1 (2003), 155--167. 7. Dranishnikov A. Groups with a polynomial dimension growth, preprint. 8. Dranishnikov A. Dimension theory local and global, preprint. 9. Dranishnikov A., Keesling J.E., Uspenskij V.V. On the Higson corona of uniformly contractible spaces Topology, 37, No. 3 (1998), 791--803. 10. Dranishnikov A., Zarichnyi M. Universal spaces for asymptotic dimension, Topology Appl. 140, No.2-3 (2004), 203--225. 11. Gromov M. Asymptotic invariants of infinite groups. Geometric group theory, Vol. 2 (Sussex, 1991), 1--295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993. 12. Ostrand Ph. A. Dimension of metric spaces and Hilbert's problem $13$, Bull. Amer. Math. Soc. 71 (1965), 619--622.
Pages	100-104
Volume	27
Issue	1
Year	2007
Journal	Matematychni Studii
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