Bourbaki's Fixpoint Lemma reconsidered
Banaschewski, Bernhard
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 303-309 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1992-01-01
Classification:  04A05,  06A06,  06A15,  06B23,  06B30,  18B25,  54A99,  54B99,  54H99 
@article{118498,
     author = {Bernhard Banaschewski},
     title = {Bourbaki's Fixpoint Lemma reconsidered},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {303-309},
     zbl = {0779.06004},
     mrnumber = {1189661},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118498}
}

Banaschewski, Bernhard. Bourbaki's Fixpoint Lemma reconsidered. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 303-309. http://gdmltest.u-ga.fr/item/118498/

Banaschewski B. Another look at the localic Tychonoff Theorem, Comment. Math. Univ. Carolinae 29 (1988), 647-656. (1988) | MR 0982782 | Zbl 0667.54009

Johnstone P.T. Topos Theory, Academic Press, London-New York-San Francisco, 1977. | MR 0470019 | Zbl 1071.18002

Johnstone P.T. Stone Spaces, Cambridge University Press, 1982. | MR 0698074 | Zbl 0586.54001

Vermeulen J.J.C. A note on iterative arguments in a topos, preprint, 1990. | MR 1131478 | Zbl 0767.18003

Vermeulen J.J.C. Some constructive results related to compactness and the (strong) Hausdorff property for locales, preprint, 1991. | MR 1173026 | Zbl 0739.18001

Witt E. Beweisstudien zum Satz von M. Zorn, Math. Nachr. 4 (1951), 434-438. (1951) | MR 0039776 | Zbl 0042.05002