A lattice naturally associated with a topological space

**Abstract**

Let *X* be a Tchonoff space. The ring of continuous real valued
functions to the reals, *C*(*X*) is well-known to be a
lattice. We exhibit a bigger lattice of real-valued functions which is
von-Neumann regular, and an epimorphic
extension of *C*(*X*).

The work dates back to a collaboration with Woods and Henriksen.