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Title: The category of compactifications and its coreflections (English)
Author: Hager, Anthony W.
Author: Wynne, Brian
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 63
Issue: 3
Year: 2022
Pages: 365-378
Summary lang: English
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Category: math
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Summary: We define ``the category of compactifications'', which is denoted {\bf{CM}}, and consider its family of coreflections, denoted {\bf{corCM}}. We show that {\bf{corCM}} is a complete lattice with bottom the identity and top an interpretation of the Čech--Stone $\beta$. A $c \in${\bf{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 in {\bf{corCM}} (thus {\bf{corCM}} is not a set), show that any $c \in${\bf{corCM}} not the identity is above an atom, and that $\beta$ is not the supremum of atoms. (English)
Keyword: compactification
Keyword: coreflection
Keyword: atom in a lattice
MSC: 06B23
MSC: 18A40
MSC: 54B30
MSC: 54C10
MSC: 54D35
idZBL: Zbl 07655806
idMR: MR4542795
DOI: 10.14712/1213-7243.2022.024
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Date available: 2023-02-01T12:11:11Z
Last updated: 2024-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151482
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