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complete lattice; closure operator; fixpoint; frame coproduct; compact frame
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.
[1] Banaschewski B.: Another look at the localic Tychonoff Theorem. Comment. Math. Univ. Carolinae 29 (1988), 647-656. MR 0982782 | Zbl 0667.54009
[2] Johnstone P.T.: Topos Theory. Academic Press, London-New York-San Francisco, 1977. MR 0470019 | Zbl 1071.18002
[3] Johnstone P.T.: Stone Spaces. Cambridge University Press, 1982. MR 0698074 | Zbl 0586.54001
[4] Vermeulen J.J.C.: A note on iterative arguments in a topos. preprint, 1990. MR 1131478 | Zbl 0767.18003
[5] Vermeulen J.J.C.: Some constructive results related to compactness and the (strong) Hausdorff property for locales. preprint, 1991. MR 1173026 | Zbl 0739.18001
[6] Witt E.: Beweisstudien zum Satz von M. Zorn. Math. Nachr. 4 (1951), 434-438. MR 0039776 | Zbl 0042.05002
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