A version of the Stone-Weierstrass Theorem asserts: If A is a linear subspace of C(K), the set of continuous functions on a compact space, and if A is a subalgebra that contains the constant functions and separates points, then A is dense in C(K) relative to the uniform (or sup-norm) topology. I am looking for a version for cones along the lines: if A is a subcone of X, itself a cone in C(K), if A is closed with respect to products, and if it contains constants and separates points in K, then A is ``dense'' in X. An example, would be the statement that the set of nondecreasing polynomials on [0,1] is dense in the set of nondecreasing continuous functions on [0,1]. (Is this true?)
I would appreciate references to such results, or to counterexamples.