  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 $X^2$ 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.
