Practice problem

General Topology

Let $X$ be a topological space and $p,\xi\in X$ points such that $p$ is a specialization of $\xi$ , meaning $p$ lies in the closure of $\xi$ as a singleton set.

If $U$ and $C$ are open and closed subsets of $X$ , respectively, what can you say about the relative containment of $p,\xi$ in $U$ and $C$ ? Mark all true implications.