Pseudocompact $σ$-frames

Year, pages: 2015, 301 - 312

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.

Clarke, J., Gilmour, C. 2015. Pseudocompact $σ$-frames. In Mathematica Slovaca, vol. 65, no.2, pp. 301-312. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0024

Clarke, J., Gilmour, C. (2015). Pseudocompact $σ$-frames. Mathematica Slovaca, 65(2), 301-312. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0024