This paper is concerned with
uniformly closed sets of continuous real-valued functions defined on a compact
Hausdorff space that are at the same time semi-algebras (wedges closed under
multiplication) and lower semi-lattices. The principal result is that any such set can
be represented as an intersection of lower semi-lattice semi-algebras of three
elementary types. This is an adaptation of a similar theorem of Choquet
and Deny for lower semi-lattice wedges. A modified form of the theorem is
also given for the case that the lower semi-lattice semi-algebra is in fact a
lattice.
