Closure_of_Finite_Union_equals_Union_of_Closures

Let $T$ be a topological space. Let $n \in \N$. Let $\forall i \in \set {1, 2, \ldots, n}: H_i \subseteq T$ Then $\displaystyle \bigcup_{i \mathop = 1}^n \map \cl {H_i} = \map \cl {\bigcup_{i \mathop = 1}^n H_i}$