@article{Protasov_2004, title={Resolvability of ball structures}, volume={5}, url={https://polipapers.upv.es/index.php/AGT/article/view/1969}, DOI={10.4995/agt.2004.1969}, abstractNote={<p>A ball structure is a triple B = (X, P, B) where X, P are nonempty sets and, for any x âˆˆ X, α âˆˆ P, B(x, α) is a subset of X, which is called a ball of radius α around x. It is supposed that x âˆˆ B(x, α) for any x âˆˆ X, α âˆˆ P. A subset Y <span style="text-decoration: underline;">C</span> X is called large if X = B(Y, α) for some α âˆˆ P where B(Y, α) = U<sub>y</sub><sub>âˆˆ</sub><sub>Y</sub> 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.</p>}, number={2}, journal={Applied General Topology}, author={Protasov, Igor V.}, year={2004}, month={Oct.}, pages={191–198} }