On some density theorems in regular vector lattices of continuous functions

In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions defined on a locally compact Hausdorff space, which we introduced and studied in [3, 4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the socalled generalized affine functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by a subset of a regular vector lattice. As a consequence, we obtain some density results. Finally, a connection with the Korovkin type approximation theory is also shown