Abstract
We consider realcompactness of frames on the basis of their cozero parts. Consequently we can (a) describe the corresponding coreflection as the relatively spatial reflection of the Lindelöf coreflection of the frame, and (b) characterize realcompactness by the elegant condition that every Cauchy filter in an appropriate uniformity be convergent. We relate the above to a frame analogue of Nachbin's approach to realcompact spaces and discuss the zero-dimensional analogue of realcompactness in the frame setting.
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Banaschewski, B., Gilmour, C. Realcompactness and the Cozero Part of a Frame. Applied Categorical Structures 9, 395–417 (2001). https://doi.org/10.1023/A:1011225712426
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DOI: https://doi.org/10.1023/A:1011225712426