Remarks on the Function Ring Functor
by
Bernhard Banaschewski
McMaster University and University of Cape Town

The aim is to show how much already follows from the most immediate properties of the functor R, which assigns to each completely regular frame L the lattice-ordered ring RL of all real-valued continuous functions on L, with analogous considerations for the ring ZL of continuous integer-valued functions on a zero-dimensional frame L. Among other things, this leads to remarkably simple proofs of the pointfree versions of classical results on realcompactness and N-compactness.

Date received: December 22, 2002