The -reflection of 0-dimensional frames

The main results here are that(i) 0 -frames are reflective in the category of all 0-dimensional frames, where a P 0 -frame is a 0-dimensional frame in which any countable join of complemented elements is complemented, and frames, meaning the completely regular frames in which every cozero element is complemented, are the same as the strongly 0-dimensional P 0 -frames. ition, it is shown that the Lindelِf and the spatial P 0 -frames are actually P-frames, but whether this holds for all P 0 -frames remains open. Finally, a simple modification of the proof of (i) is described which provides a new proof that the P-frames are reflective in the category of all completely regular frames.