Cellular balleans

O.I.Protasova

We prove that a ballean is cellular if and only if its asymptotic Gromov dimension is $0$. We construct also a universal countable metrizable ballean and show that every separable non-Archimedean metric space is asymptotically embeddable into a Hilbert space.

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

2. Dranishnikov A., Zarichnyi M. Universal spaces for asymptotic dimention. Topol. Appl. 140 (2004), no.2-3, 203–225.

3. Gromov M. Asymptotic invariants of infinite groups , London Math. Soc. Lecture Note Ser. 182 (1993).

4. Higson N., Roe J. Amenable group actions and the Novikov conjecture, J. reine angew. Math, 519 (2000), 143--135.

5. Mitchener P.D. Coarse Homology Theories, Algebr. Geom. Topology, 1 (2001), 271--297.

6. Protasov I., Banakh T. Ball Structures and Colorings of Graphs and Groups, Matem. Stud. Monogr. Ser., Vol. 11, 2003.

7. Protasov I.V. Metrizable ball structures, Algebra and Discrete Math.(2002), no.1, 129--141.

8. Roe J. Lectures on Coarse Geometry, AMS University Lecture Series, 31, 2003.

9. Sarnak P. What is ... an expander?, Notices of AMS, 51 (2004), 762--763.

	Cellular balleans
Author	O.I.Protasova polla@unicyb.kiev.ua Department of Cybernetics,Kyiv National University
Abstract	We prove that a ballean is cellular if and only if its asymptotic Gromov dimension is $0$. We construct also a universal countable metrizable ballean and show that every separable non-Archimedean metric space is asymptotically embeddable into a Hilbert space.
Keywords	celluar balleans, asymptotic Gromov dimension, countable metrizable ballean
DOI	doi:10.30970/ms.25.1.3-9
Reference	1. Dranishnikov A. Asymptotic topology, Russian Math. Surveys, 55 (2000), no. 6, 71--116. 2. Dranishnikov A., Zarichnyi M. Universal spaces for asymptotic dimention. Topol. Appl. 140 (2004), no.2-3, 203–225. 3. Gromov M. Asymptotic invariants of infinite groups , London Math. Soc. Lecture Note Ser. 182 (1993). 4. Higson N., Roe J. Amenable group actions and the Novikov conjecture, J. reine angew. Math, 519 (2000), 143--135. 5. Mitchener P.D. Coarse Homology Theories, Algebr. Geom. Topology, 1 (2001), 271--297. 6. Protasov I., Banakh T. Ball Structures and Colorings of Graphs and Groups, Matem. Stud. Monogr. Ser., Vol. 11, 2003. 7. Protasov I.V. Metrizable ball structures, Algebra and Discrete Math.(2002), no.1, 129--141. 8. Roe J. Lectures on Coarse Geometry, AMS University Lecture Series, 31, 2003. 9. Sarnak P. What is ... an expander?, Notices of AMS, 51 (2004), 762--763.
Pages	3-9
Volume	25
Issue	1
Year	2006
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html