Separating set

A set of functions $𝑆 \subseteq {(} 𝑋, 𝑌)$ is said to separate the points of $𝑋$ iff for every $𝑥, 𝑦 \in 𝑋$ there exists an $𝑓 \in 𝑆$ such that $𝑓 (𝑥) \neq 𝑓 (𝑦)$ . fun