A Note On Separating Function Sets

الأصل · EN

We study separating function sets. We find some necessary and sufficient conditions for Cₚ(X) or Cₚ²(X) to have a point-separating subspace that is a metric space with certain nice properties. One of the corollaries to our discussion is that for a zero-dimensional X, Cₚ(X) has a discrete point-separating space if and only if Cₚ²(X) does.