Splitting of closed subgroup

Question

A closed subgroup $H$ of a topological abelian group $G$ is called split if there exist a continuous homomorphism $f:G\to H$ such that $f\mid{H}=1\mid{H}$. Let $G$ and $G'$ were two topological abelian groups. Let $K$ be a closed subgroup of $G\bigoplus G'$ such that $\pi_{1}(K)$ and $\pi_{2}(K)$ split in $G$ and $G'$, respectively. Is $K$ split in $G\bigoplus H$?