Article
| 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: | 2023-04-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151482 |
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