On normal functions

AbstractDilworth defined normal (upper semicontinuous) functions in [2] and used them to describe the Dedekind completion of C∗(X), the lattice of bounded continuous real-valued functions on a completely regular Hausdorff space X. In this paper we present some new properties of normal functions which enable us to view certain sets of normal functions defined on a Baire space as direct limits of sets of continuous functions. This provides various operations on normal functions and, in turn, a connection with some of the rings studied by Fine et al. in [3]