Sketch of vector balleans

Ie.Lutsenko; I.V.Protasov

A ballean is a set $X$ endowed with some family of subsets of $X$ which are called the balls. We postulate the properties of the family of balls in such a way that the balleans with appropriate morphisms can be considered as asymptotic counterparts of uniform spaces. The purpose of the paper is to find the asymptotic counterparts for topological vector spaces.

1. D.~Dikranian, I.~Protasov, Maximal vector topologies, preprint.

2. M.~Filali, Ie.~Lutsenko, I.V.~Protasov, Boolean group ideals and the ideal structure of $\beta G$, Mat. Stud. 31 (2009) №1, 19--28.

3. V.~Frider, M.~Zarichnyi, On coarse anti-Lawson semilattices, Mat. Stud. 21 (2004) №1, 3--12.

4. M.~Ostrovskii, Coarse embeddability into Banach spaces, Topology Proc. 33 (2009) 163-183.

5. I.~Protasov, O.~Protasova, Sketch of group balleans, Mat. Stud. 22 (2004) №1, 10--20.

6. I.~Protasov, M.~Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., Vol. 12, VNTL, Lviv, 2007.

7. J.~Roe, Lectures on Coarse Geometry, University Lecture Series, 31, Amer. Math. Soc., Providence, RI, 2003.

	Sketch of vector balleans
Author	Ie.Lutsenko, I.V.Protasov protasov@unicyb.kiev.ua Department of Cybernetics,Kyiv National University, Volodimirska 64, Kyiv 01033, Ukraine
Abstract	A ballean is a set $X$ endowed with some family of subsets of $X$ which are called the balls. We postulate the properties of the family of balls in such a way that the balleans with appropriate morphisms can be considered as asymptotic counterparts of uniform spaces. The purpose of the paper is to find the asymptotic counterparts for topological vector spaces.
Keywords	ballean, morphism, asymptotic counterpart, uniform space
DOI	doi:10.30970/ms.31.2.219-224
Reference	1. D.~Dikranian, I.~Protasov, Maximal vector topologies, preprint. 2. M.~Filali, Ie.~Lutsenko, I.V.~Protasov, Boolean group ideals and the ideal structure of $\beta G$, Mat. Stud. 31 (2009) №1, 19--28. 3. V.~Frider, M.~Zarichnyi, On coarse anti-Lawson semilattices, Mat. Stud. 21 (2004) №1, 3--12. 4. M.~Ostrovskii, Coarse embeddability into Banach spaces, Topology Proc. 33 (2009) 163-183. 5. I.~Protasov, O.~Protasova, Sketch of group balleans, Mat. Stud. 22 (2004) №1, 10--20. 6. I.~Protasov, M.~Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., Vol. 12, VNTL, Lviv, 2007. 7. J.~Roe, Lectures on Coarse Geometry, University Lecture Series, 31, Amer. Math. Soc., Providence, RI, 2003.
Pages	219-224
Volume	31
Issue	2
Year	2009
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html