The P-0-reflection of 0-dimensional frames

作者：Banaschewski B^*

来源：Topology and Its Applications, 2014, 168: 16-24.

DOI：10.1016/j.topol.2014.02.018

• Complemented elements
• 0-dimensional frame
• Strongly 0-dimensional frame
• P-frame

The main results here are that
(i) the P-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
(ii) the P-frames, meaning the completely regular frames in which every cozero element is complemented, are the same as the strongly 0-dimensional P-0-frames.
In addition, it is shown that the Lindelof 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.

• 出版日期2014-5-15