Abstract
We establish a version of the Shirota Theorem which characterises realcompactness in terms of completeness for frames; an interesting problem considering the various notions of realcompactness for frames and the fact that the frame completion behaves differently from its spatial counterpart. Amongst other consequences of this characterisation, we can describe the completion of a uniform sigma frame. We highlight some differences between frames and spaces when considering the Lindelöf property, realcompactness, paracompactness and completeness. Most of these results appear in the doctoral thesis of the author.
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Walters-Wayland, J.L. A Shirota Theorem for Frames. Applied Categorical Structures 7, 271–277 (1999). https://doi.org/10.1023/A:1008670918544
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DOI: https://doi.org/10.1023/A:1008670918544