(or just to separate points) if for any two distinct elements
[1] 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.
[1] This mathematical logic-related article is a stub.