Functors of finite degree and asymptotic dimension zero

O.Shukel'

For any finitary normal functor $F$ in the category of compact Hausdorff spaces one can define its counterpart on the category of proper metric spaces and coarse maps. The aim of this note is to show that the obtained functor preserves the class of proper metric spaces of asymptotic dimension zero in the sense of Gromov.

1. E.V. Shchepin. Functors and uncountable powers of compacta // Uspekhi Mat. Nauk. -- 1981.-- V. 36, № 3. -- P.3--62.

2. Frider V. Normal functors in coarse category // Algebra and Discrete Mathematics. -- 2005. -- № 4. -- P.16--27.

3. Gromov M. Asymptotic invariants for infinite groups// LMS Lecture Notes. -- 1993. -- V. 182, № 2. -- P. 1--295.

4. Шукель О. Гiперсиметричнi степенi i асимптотично нульвимiрнi простори// Вiсник Львiвського унiверситету, сер. мех.-мат. -- 2006. -- Вип. 66. -- С.214--224.

5. Dranishnikov A. Asymptotic topology// Russian Math. Surveys. -- 2000. -- V. 55, № 6. -- P.71--116.

6. M. M. Zarichnyi. On covariant topological functors, I. // Q $\&$ A in General Topology. -- 1991. -- V. 8. -- P.1--32.

7. Brodskiy N., Dydak J., Higes J., Mitra A. Dimention zero at all scales// Topology Appl. -- 2007. -- V.154, № 14. -- P.2729 -- 2740.

8. Basmanov V. N. Covariant functors, retracts, and dimension // Dokl. Akad. Nauk SSSR. -- 1983. -- V.271, № 5. -- P.1033--1036 (Russian).

9. Basmanov V. N. Dimension and some functors with finite support // Vestnik Moskov. Univ. Ser. I Mat. Mekh. -- 1981. -- № 6. -- P.48--50 (Russian).

	Functors of finite degree and asymptotic dimension zero
Author	O.Shukel' Faculty of Mechanics and Mathematics,Ivan Franko National University of L'viv
Abstract	For any finitary normal functor $F$ in the category of compact Hausdorff spaces one can define its counterpart on the category of proper metric spaces and coarse maps. The aim of this note is to show that the obtained functor preserves the class of proper metric spaces of asymptotic dimension zero in the sense of Gromov.
Keywords	functor, finite degree, asymptotic dimension zero
DOI	doi:10.30970/ms.29.1.101-107
Reference	1. E.V. Shchepin. Functors and uncountable powers of compacta // Uspekhi Mat. Nauk. -- 1981.-- V. 36, № 3. -- P.3--62. 2. Frider V. Normal functors in coarse category // Algebra and Discrete Mathematics. -- 2005. -- № 4. -- P.16--27. 3. Gromov M. Asymptotic invariants for infinite groups// LMS Lecture Notes. -- 1993. -- V. 182, № 2. -- P. 1--295. 4. Шукель О. Гiперсиметричнi степенi i асимптотично нульвимiрнi простори// Вiсник Львiвського унiверситету, сер. мех.-мат. -- 2006. -- Вип. 66. -- С.214--224. 5. Dranishnikov A. Asymptotic topology// Russian Math. Surveys. -- 2000. -- V. 55, № 6. -- P.71--116. 6. M. M. Zarichnyi. On covariant topological functors, I. // Q $\&$ A in General Topology. -- 1991. -- V. 8. -- P.1--32. 7. Brodskiy N., Dydak J., Higes J., Mitra A. Dimention zero at all scales// Topology Appl. -- 2007. -- V.154, № 14. -- P.2729 -- 2740. 8. Basmanov V. N. Covariant functors, retracts, and dimension // Dokl. Akad. Nauk SSSR. -- 1983. -- V.271, № 5. -- P.1033--1036 (Russian). 9. Basmanov V. N. Dimension and some functors with finite support // Vestnik Moskov. Univ. Ser. I Mat. Mekh. -- 1981. -- № 6. -- P.48--50 (Russian).
Pages	101-107
Volume	29
Issue	1
Year	2008
Journal	Matematychni Studii
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Table of content of issue	html