Free uniformly complete vector lattices

We define a free uniformly complete vector lattice \(\text {FUCVL}(A)\) $\text{FUCVL}(A)$ over a non-empty set A and give its representation as a sublattice of the space \(H(\mathbb {R}^A)\) $H({\mathbb{R}}^A)$ of continuous in the product topology positively homogeneous functions on \(\mathbb {R}^A\) ${\mathbb{R}}^A$ .