Regularity and transitivity of local-automorphism semigroups of locally finite forests
We show that any open Riemann surface can be properly immersed in any Stein manifold with the (Volume) Density property and of dimension at least 2. If the dimension is at least 3, we can actually choose this immersion to be an embedding. As an application, we show that Stein manifolds with the (Volume) Density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.
Second centralizers of partial transformations on a finite set are determined. In particular, it is shown that the second centralizer of any partial transformation consists of partial transformations that are locally powers of .