Let $T$ be a topological semigroup and $K$ be a compact set in $T$. I know that if $T=(\mathbb{R}^n, +)$ or $T=(\mathbb{Z}^n, +)$, then for every compact set $K$ in $T$, there is compact set $S$ with $SK\subseteq (T-K)$. What can say about other topological semigroups?
Can we say that it does hold for any topological semigroup? Please help me to know it.