Abstract:A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a $\sigma $-frame and to Alexandroff spaces.
Keywords: pseudocompact frames, $\sigma $-frames, cozero elements and Alexandroff spaces
AMS Subject Classification: 54C50, 54D20, 06B10