Vol. 18, No. 1, 1966

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Semi-algebras that are lower semi-lattices

Edward Joseph Barbeau

Vol. 18 (1966), No. 1, 1–7

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.

Mathematical Subject Classification
Primary: 46.06
Secondary: 46.55
Received: 26 February 1965
Published: 1 July 1966
Edward Joseph Barbeau