| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-02-01T12:11:11Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151482 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
