Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

A completely regular topological space 𝑋 is called a 𝑃-space if every zero-set in 𝑋 is open. An intermediate ring is a ring 𝐴(𝑋) of real-valued continuous functions on 𝑋 containing all the ...