Pseudocompact σ-Frames

Abstract

Abstract The cozero part of a sigma-frame is considered here for the first time. The fundamental notion of a trail in a frame is adapted for sigma-frames via the notion of a witness and, as a consequence, one obtains characterisations for the cozero elements, and of pseudocompactness, of sigma-frames. In the presence of complete regularity, pseudocompactness is seen to be equivalent to (countable) compactness which, in this setting, and unlike its spatial and frame counterparts, gives rise to a coreflection which is the pseudocompactification.