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 | | Title: Ball Structures and Colorings of Graphs and Groups |
| Authors: I. Protasov, T. Banakh |
| ISBN: 966-7148-99-8 |
| Price: 14.50 USD |
The ball structures of different kinds arise naturally in the asymptotic topology, geometric group theory and combinatorics. The book is devoted to systematic investigation of purely combinatorical aspects of ball structures of graphs with accent on their applications to partitions of groups and graphs. A lot of new author’s results are included. An exposition is supplied with a chain of exercises and open problems.
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 | | Title: General Asymptology |
| Authors: Ihor Protasov, Michael Zarichnyi |
| ISBN: 966-8849-32-9 |
| Price: 35.00 USD |
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 close to the non-Archimedean (ultrametric) spaces. Chapter 4 is devoted to the property of normality. In Chapters 5 and 6 the graph balleans and the group balleans are investigated. In Chapter 7 the functions on balleans which are slowly oscillating with respect to given filter are studied. The counterpart of the Higson corona in the context of balleans is investigated in Chapter 8. Some cardinal invariants of balleans are introduced and discussed in Chapter 9. The concluding Chapter 10 is devoted to the notion of maximality of balleans. Bibliography: 86 items.
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