On P-sober Spaces.

In this paper, we focus on p-sober spaces and prove that (1) the T0 space X is p-sober if and only if the Smyth power space of X is p-sober; (2) the space X has a p-sober dcpo model if and only if X is T1 and p-sober; (3) every non-p-sober T0 space does not have a p-sobrification; (4) the T0 space X is sober if and only if X is p-sober and PD. [ABSTRACT FROM AUTHOR]