 Separating set

In mathematics a set of functions "S" from a set "D" to a set "C" is called a separating set for "D" or said to separate the points of "D" if for any two distinct elements "x" and "y" of "D", there exists a function "f" in "S" so that "f"("x") ≠ "f"("y").Separating sets can be used to formulate a version of the Stone-Weierstrass theorem for real-valued functions on a compact Hausdorff space "X", with the topology of uniform convergence.