Asymptotic proximities

Authors

  • Igor V. Protasov Kyiv University

DOI:

https://doi.org/10.4995/agt.2008.1799

Keywords:

Ballean, Determining covering, Proximity

Abstract

A ballean is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that the balleans can be considered as a natural asymptotic counterparts of the uniform topological spaces. We introduce and study an asymptotic proximity as a counterpart of proximity relation for uniform topological space.

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Author Biography

Igor V. Protasov, Kyiv University

Departament of Cybernetics

References

A. Dranishnikov, Asymptotic topology, Russian Math. Surveys 55 (2000), 71–116.

http://dx.doi.org/10.1070/RM2000v055n06ABEH000334

R. Engelking, General Topology, PWN, Warszava, 1985.

M. Filali and I. V. Protasov, Slowly oscillating function on locally compact groups, Applied General Topology 6, no. 1 (2005) 67-77.

I. V. Protasov and T. Banakh, Ball Structures and Colorings of Groups and Graphs, Math. Stud. Monogr. Ser. V.11, 2003.

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

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How to Cite

[1]
I. V. Protasov, “Asymptotic proximities”, Appl. Gen. Topol., vol. 9, no. 2, pp. 189–195, Oct. 2008.

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Articles