| Title:
|
Completeness properties of function rings in pointfree topology (English) |
| Author:
|
Banaschewski, Bernhard |
| Author:
|
Hong, Sung Sa |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
245-259 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or $\sigma$-comp\-lete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions. (English) |
| Keyword:
|
frame of reals |
| Keyword:
|
lattice ordered rings of real valued continuous functions and integer valued continuous functions |
| Keyword:
|
extremally disconnected frame |
| Keyword:
|
basically disconnected frame |
| Keyword:
|
cozero map |
| MSC:
|
06D22 |
| MSC:
|
54C30 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 1098.06006 |
| idMR:
|
MR2026162 |
| . |
| Date available:
|
2009-01-08T19:29:08Z |
| Last updated:
|
2020-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119384 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Banaschewski B.: The real numbers in pointfree topology.Textos de Matemática Série B, No. 12, Departamento de Matemática da Universidade de Coimbra, 1997. Zbl 0891.54009, MR 1621835 |
| Reference:
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| Reference:
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| Reference:
|
[7] Johnstone P.T.: Conditions related to De Morgan's law.In Applications of Sheaves, Proceedings, Durham, 1977, Springer LNM 753 (1979), pp. 479-491. Zbl 0445.03041, MR 0555556 |
| Reference:
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| Reference:
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[9] Nakano H.: Über das System aller stetigen Funktionen auf einen topologischen Raum.Proc. Imp. Acad. Tokyo 17 (1941), 308-310. MR 0014173 |
| Reference:
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[10] Stone M.H.: Boundedness properties in function lattices.Canad. J. Math. 1 (1949), 176-186. Zbl 0032.16901, MR 0029091, 10.4153/CJM-1949-016-5 |
| Reference:
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| . |
