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).

Examples

• The singleton set consisting of the identity function on R separates the points of R.

• If X is a normal topological space, then Urysohn's lemma states that the set C(X) of continuous functions on X with real (or complex) values separates points on X.

See also

• Stone-Weierstrass theorem