Sum of Closures is Subset of Closure of Sum in Topological Vector Space

Theorem
Let $K$ be a topological field.

Let $X$ be a topological vector space over $K$.

Let $A, B \subseteq X$.

Then:


 * $A^- + B^- \subseteq \paren {A + B}^-$

where $A^-$, $B^-$ and $\paren {A + B}^-$ denote the closures of $A$, $B$ and $A + B$.