### Resolvability of ball structures

#### Abstract

A ball structure is a triple B = (X, P, B) where X, P are nonempty sets and, for any x ∈ X, α ∈ P, B(x, α) is a subset of X, which is called a ball of radius α around x. It is supposed that x ∈ B(x, α) for any x ∈ X, α ∈ P. A subset Y C X is called large if X = B(Y, α) for some α ∈ P where B(Y, α) = U_{y}_{∈}_{Y} B(y, α). The set X is called a support of B, P is called a set of radiuses. Given a cardinal k, B is called k-resolvable if X can be partitioned to k large subsets. The cardinal res B = sup {k : B is k-resolvable} is called a resolvability of B. We determine the resolvability of the ball structures related to metric spaces, groups and filters.

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1. **Asymptotic structures of cardinals**

Oleksandr Petrenko, Igor V. Protasov, Sergii Slobodianiuk** Applied General Topology** vol: 15 issue: 2 first page: 137 year: 2014

doi: 10.4995/agt.2014.3109

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 |