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VNTL Publishers, 2007 8vo (21.5 cm), 219 pp. Laminated boards. The present monograph is devoted mostly to general properties of the ball structures, which simultaneously generalize the coarse structures introduced in the large scale geometry by J. Roe as well as the uniform structures. Chapter 1 contains the definition of the ball structures (baleans), provides their different examples and briefly discusses their connections with coarse structures. The topological coarse structures are also considered. The different morphisms of balleans and coarse spaces are defined and some categories of balleans and coarse structures are introduced. Chapter 2 is devoted to relations between the ball structures and metric structures, important morphisms between metric spaces. Chapter 3 concerns the property of cellularity of balleans and contains the notion of asymptotic dimension of balleans in the spirit of Gromov. It turns out that cellularity can be described in terms of asymptotic dimension zero, which makes it… Read More