Maximal balleans

Olga I. Protasova

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 the appropriate morphisms can be considered as the asymptotic counterparts of the uniform topological spaces. The purpose of the paper is to find and study the asymptotic counterparts for maximal topological spaces and maximal topological groups.


Keywords

Ballean; Ball structure; Ballean envelope; group ideal

Full Text:

PDF

References

W. W. Comfort, O. Masaveau and H. Zhou, Resolvability in Topology and in Topological groups, Annals of New York Acad. of Sciences, 767 (1995), 17-27. http://dx.doi.org/10.1111/j.1749-6632.1995.tb55890.x

W. W. Comfort and S. García-Ferreira, Resolvability: a selective survey and some new results, Topology Appl. 74 (1996), 149-167. http://dx.doi.org/10.1016/S0166-8641(96)00052-1

A. Dranishnikov, Asymptotic topology, Russian Math. Survey 55 (2000), 71-116. http://dx.doi.org/10.1070/RM2000v055n06ABEH000334

N. Hidman and D. Strauss, Algebra in the Stone-Cech Compactification, de Grueter Exposition in Math., V.27, 1998.

V. I. Malykhin, Extremally disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21-25.

P. D. Mitchener, Coarse Homology Theories, Algebr. Geom. Topology, 1 (2001), 271- 294. http://dx.doi.org/10.2140/agt.2001.1.271

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

I. V. Protasov, Filters and topologies on groups, Mat. Stud. 3 (1994), 15-28.

I. V. Protasov, Resolvability of groups, Mat. Stud. 9 (1998), 130-148.

I. V. Protasov, Maximal topologies on groups, Sib. Math. J. 39 (1998), 1368-1381. http://dx.doi.org/10.1007/BF02674129

I. V. Protasov, Metrizable ball structures, Algebra and Discrete Math., 2002, N1, 129-141.

I. V. Protasov, Uniform ball structures, Algebra and Discrete Math, 2003, N1, 93-102.

I. V. Protasov, Normal ball structures, Mat. Stud. 20 (2003), 3-16.

I. V. Protasov, Morphisms of ball structures of groups and graphs, Ukr. Math. J. 54 (2002), 847-855.

I. V. Protasov, Coronas of balleans, Topology Appl.149(2005), 149-160. http://dx.doi.org/10.1016/j.topol.2004.09.005

I. V. Protasov, Resolvability of ball structures, Appl. Gen. Topology 5 (2004), 191-198.

I. V. Protasov and O. I. Protasova, Sketch of group balleans, Mat. Stud. 22 (2004), 10-20.

O. I. Protasova, Ball structures of G-spaces, Bulletin of the University of Kiev, Series: Physics and Math., 2004, 3, 54-69.

J. Roe, Lectures in Coarse Geometry, AMS University Lecture Series, 31 (2004).

Abstract Views

869
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt