| Title:
|
Bourbaki's Fixpoint Lemma reconsidered (English) |
| Author:
|
Banaschewski, B. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
303-309 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A constructively valid counterpart to Bourbaki's Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice $L$ to be stable under another closure operator of $L$. This is then used to deal with coproducts and other aspects of frames. (English) |
| Keyword:
|
complete lattice |
| Keyword:
|
closure operator |
| Keyword:
|
fixpoint |
| Keyword:
|
frame coproduct |
| Keyword:
|
compact frame |
| MSC:
|
04A05 |
| MSC:
|
06A06 |
| MSC:
|
06A15 |
| MSC:
|
06B23 |
| MSC:
|
06B30 |
| MSC:
|
18B25 |
| MSC:
|
54A99 |
| MSC:
|
54B99 |
| MSC:
|
54H99 |
| idZBL:
|
Zbl 0779.06004 |
| idMR:
|
MR1189661 |
| . |
| Date available:
|
2009-01-08T17:55:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118498 |
| . |
| Reference:
|
[1] Banaschewski B.: Another look at the localic Tychonoff Theorem.Comment. Math. Univ. Carolinae 29 (1988), 647-656. Zbl 0667.54009, MR 0982782 |
| Reference:
|
[2] Johnstone P.T.: Topos Theory.Academic Press, London-New York-San Francisco, 1977. Zbl 1071.18002, MR 0470019 |
| Reference:
|
[3] Johnstone P.T.: Stone Spaces.Cambridge University Press, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[4] Vermeulen J.J.C.: A note on iterative arguments in a topos.preprint, 1990. Zbl 0767.18003, MR 1131478 |
| Reference:
|
[5] Vermeulen J.J.C.: Some constructive results related to compactness and the (strong) Hausdorff property for locales.preprint, 1991. Zbl 0739.18001, MR 1173026 |
| Reference:
|
[6] Witt E.: Beweisstudien zum Satz von M. Zorn.Math. Nachr. 4 (1951), 434-438. Zbl 0042.05002, MR 0039776 |
| . |
