Cellularity and density of balleans

Igor V. Protasov

Ukraine

Kyiv University

Departament of Cybernetics

Submitted: 2013-11-18

|

Accepted: 2013-11-18

|

Published: 2013-11-18

DOI: https://doi.org/10.4995/agt.2007.1898
Funding Data

Downloads

Keywords:

Ballean, Large and thick subsets, Density, Cellularity

Supporting agencies:

This research was not funded

Abstract:

A ballean is a set X endowed with some family F of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Then we define the asymptotic counterparts for dense and open subsets, introduce two cardinal invariants (density and cellularity) of balleans and prove some results concerning relationship between these invariants. We conclude the paper with applications of obtained partitions of left topological group in dense subsets.
Show more Show less

References:

A. Bella and V. I. Malyhkin, Small and other subsets of a group, Q and A in General Topology, 11 (1999), 183–187.

T. J. Carlson, N. Hindman, J. McLeod and D. Strauss, Almost Disjoint Large Subsets of Semigroups, Topology Appl., to appear.

A. Dranishnikov, Asymptotic topology, Russian Math. Survey, 52 (2000), 71–116.

The Kourovka Notebook, Amer. Math. Soc. Transl. (2), 121, Providence, 1983.

V. I. Malykhin and I. V. Protasov, Maximal resolvability of bounded groups, Topology Appl. 73 (1996), 227–232. http://dx.doi.org/10.1016/S0166-8641(96)00020-X

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

I. V. Protasov, Uniform ball structures, Algebra and Discrete Math. 2002, N1, 129–141.

I. V. Protasov, Normal ball structures, Math. Stud. 20 (2003), 3–16.

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

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

Show more Show less