Protasova O. Balleans of G - spaces

Ballean is a set endowed with some family of its subsets which are called the balls. We postulate the properties of the family of ball in such a way that a ballean can be considered as a natural counterpart of a uniform topological space. We characterize the cellular and pseudodiscrete balleans, study the balleans of universal and finitary G - spaces, relationships between group balleans and group ideals, give some constructions of group ideals, under CH we construct a maximal group balleans, describe the maximal irresolvable balleans, calculate the detectors and asymptotic detectors of some hypergraphs. Key words: ball structure, ballean, asymorphism, cellularity, pseudodiscretness, ballean of G - space, finitary and universal G - spaces, group balleans and group ideals, ballean envelope, detector and asymptotic detector.