Schleiermachers Starrheitsbedingung für Projektivitäten in der Topologischen Geometric.
In this paper semigroups of contractions of metric spaces are considered. The semigroup of contractions of the wreath product of metric spaces is calculated.
For a one-to-one self-conformal contractive system on with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to . We give a simple proof of this result as well as discuss some further properties related to the separation condition.
Denote by , , the regular tree whose vertices have valence , its boundary. Yu. A. Neretin has proposed a group of transformations of , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that is generated by two groups: the group of tree automorphisms, and a Higman-Thompson group . We prove the simplicity of and of a family of its subgroups.