Semi-algebras that are lower semi-lattices
Edward Barbeau · Pacific Journal of Mathematics · 1966
This paper is concerned with uniformly closed sets ofcontinuous real-valued functions defined on a compactHausdorff 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 representedas an intersection of lower semi-lattice semi-algebras of threeelementary types. This is an adaptation of a similar theoremof Choquet and Deny for lower semi-lattice wedges. Amodified form of the theorem is also given for the case thatthe lower semi-lattice semi-algebra is in fact a lattice.Throughout,