A Note on Minimal Separating Function Sets

Resumo

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in C_p(X) is equivalent to having a minimal separating collection of functionally open sets in X. We also identify a nice visual property of X² that may be responsible for the existence of a minimal separating function family for X in C_p(X). We then discuss various questions and directions around the topic.