Product of compact subsets of a topological group is compact

Question

I need to show that if $G$ is a topological group and $A,B\subseteq G$ are compact subsets, then $AB$ is compact.

Thanks

Answer 1

Hint: Use the Tychonoff theorem and the continuity of the map $$G\times G\rightarrow G$$ $$(a,b)\mapsto ab$$.