… Now dimension can be related to almost every mathematical object. In this survey we consider
the asymptotic dimension … , nor do we present any applications of asymptotic dimension to …

… Thus, in Section 2 we prove the following finite union theorem for asymptotic dimension
asdimX ∪ Y ≤ max{asdimX, asdimY } whereas the classical Menger-Urysohn theorem …

… Abstract We introduce the notion of asymptotic cohomology based on the … asymptotic
dimension asdimZ X of metric spaces. We show that it agrees with the asymptotic dimension asdim …

… asymptotic dimension. Currently no example of a finitely generated group with infinite asymptotic
dimension … It should also be noted that two different definitions of asymptotic dimension …

… ’s notion of asymptotic dimension of finitely … asymptotic dimension formula for solvable
groups (§3). The main ingredient of §2 is Theorem 2.1 which states that the asymptotic dimension …

… We construct a universal space for the class of proper metric spaces of bounded
geometry and of given asymptotic dimension. As a consequence of this result, we establish …

… If an asymptotics is represented by a function that tends to a finite limit when … dimensions
appear in self-similar solutions. It is also the case that only a power-type asymptotics …

… asymptotic dimension. As applications we find upper bound estimates for the asymptotic
dimension … We are also able to improve the known upper bounds on the asymptotic dimension …

… As a corollary, we show that the asymptotic dimension of the curve … dimension of X is at
most n, but it is not at most n1. If such n does not exist, then we define the asymptotic dimension …

arXiv:math/0507570v2 [math.GR] 11 Aug 2005 Page 1 arXiv:math/0507570v2 [math.GR] 11
Aug 2005 Ы ХШЬЧЬС СХ ЦЫСЧЦ СЦ Ф ЯЧ К ФФ Ц К Ъ ЦСЫРЦСУЧЮ зиж иК Ь з зйжк н л …