-spaces and the Wallman compactification.
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is the category of spaces with filters: an object is a pair , a compact Hausdorff space and a filter of dense open subsets of . A morphism is a continuous function for which whenever . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically...