homogeneous

Let $\mathfrak M$ be a class of mappings. A space X is said to be homogeneous with respect to $\mathfrak M$ (or shortly $\mathfrak M$-homogeneous) provided that for every two points p and q of X there is a surjective mapping $f: X \to X$ such that f(p) = q and $f \in \mathfrak M$. If $\mathfrak M$ is the class of homeomorphisms, we get the concept of a homogeneous space.