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

This category contains pages concerning Sum of Closures is Subset of Closure of Sum in Topological Vector Space:

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 $A + B$.