The function ring functors of pointfree topology revisited

This paper establishes two new connections between the familiar function ring functor {\mathfrak R} on the category {\bf CRFrm} of completely regular frames and the category {\bf CR}{\mathbf \sigma}{\bf Frm} of completely regular \sigma-frames as well as their counterparts for the analogous functor {\mathfrak Z} on the category {\bf ODFrm} of ۰-dimensional frames, given by the integer-valued functions, and for the related functors {\mathfrak R}^* and {\mathfrak Z}^* corresponding to the bounded functions.  Further it is shown that some familiar facts concerning these functors are simple consequences of the present results.

Keywords:

Completely regular frames , zero dimensional frames , completely regular sigma-frames , zero dimensional sigma-frames , real-valued continuous functions and integer-valued continuous functions on frames