# The whole group is covered by compact translating of subgroups

$G$ is a locally compact (may not necessarily Hausdorff) group, $H$ is a subgroup in $G$, $G/H$ is compact as a quotient space , then there exist a compact subset $K$ such that $G=KH$(or $G=HK$).

• is G/H assumed to be hausdorff? – oxeimon Jun 10 '15 at 18:25
• Use that $G/H$ is compact. – Dietrich Burde Jun 10 '15 at 18:34
• @oxeimon: $G/H$ may not necessarily be Hausdorff. – David Chan Jun 10 '15 at 18:42