A topology on the Fremlin tensor product between locally solid vector lattices

Let $E$ and $F$ be locally solid vector lattices. In this short note, we establish a locally solid topology on the Fremlin tensor product $E\bar{\otimes }F$ and we denote it by ${\tau }_{E\bar{\otimes }F}$. It extends the Fremlin projective tensor product in the setting of Banach lattices. We show that ${\tau }_{E\bar{\otimes }F}$ is Hausdorff provided that both $E$ and $F$ are Hausdorff.