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 0-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.

The function ring functors of pointfree topology revisited 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