In mathematics, a set of functionss with domain is called a and is said to (or just

Separating sets can be used to formulate a version of the Stone–Weierstrass theorem for real-valued functions on a compact Hausdorff space with the topology of uniform convergence. It states that any subalgebra of this space of functions is dense if and only if it separates points. This is the version of the theorem originally proved by Marshall H. Stone.

Examples

• The singleton set consisting of the identity function

• is a T1 normal topological space, then Urysohn's lemma of continuous functions with real (or complex

• is a locally convex then the Hahn–Banach separation theorem implies that continuous linear functionals separate points.

See also

References