Topological Closure of Subset is Subset of Topological Closure

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq K$ and $K \subseteq S$.

Then:
 * $\operatorname{cl}\left({H}\right) \subseteq \operatorname{cl}\left({K}\right)$

where $\operatorname{cl}\left({H}\right)$ denotes the closure of $H$.