Separating set

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


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