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Resolvability of ball structures

By Igor V. Protasov

Abstract

[EN] 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) = Uy∈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.Protasov, IV. (2004). Resolvability of ball structures. Applied General Topology. 5(2):191-198. doi:10.4995/agt.2004.1969.SWORD1911985

Topics: Ball structures, Resolvability, Coresolvability
Publisher: 'Universitat Politecnica de Valencia'
Year: 2004
DOI identifier: 10.4995/agt.2004.1969
OAI identifier: oai:riunet.upv.es:10251/82558
Provided by: RiuNet
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