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The category of compactifications and its coreflections

Anthony W. Hager, Brian Wynne (2022)

Commentationes Mathematicae Universitatis Carolinae

We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone β . A c corCM implies the assignment to each locally compact, noncompact Y a compactification minimum for membership in the “object-range” of c . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...

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