Copies of ${\mathbb{R}}^{\mathbb{N}}$ in F-lattices

Modifying ideas presented in [14] we prove that a complete metrizable locally solid Riesz space $E$ contains a linear subspace linearly homeomorphic to ${\mathbb{R}}^{\mathbb{N}}$ iff $E$ contains a sublattice order isomorphic to ${\mathbb{R}}^{\mathbb{N}}$.