Range sets and partition sets in connection with congruences and algebraic invariants.
For an arbitrary permutation in the semigroup of full transformations on a set with elements, the regular elements of the centralizer of in are characterized and criteria are given for to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.
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.