Given a space $X$ and $C \subset X$, we say that $C$ is strongly discrete if there exists a disjoint family $\{U_x: x\in C\} $ of open sets in $X$ such that $x\in U_x$ for all $x\in C$. The question is this:
How to show any convergent sequence is strongly discrete in Hausdorff space?
Thanks ahead.