Bourbaki's Fixpoint Lemma reconsidered

Bernhard Banaschewski

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 303-309
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Banaschewski, Bernhard. "Bourbaki's Fixpoint Lemma reconsidered." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 303-309. <http://eudml.org/doc/247356>.

@article{Banaschewski1992,
abstract = {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.},
author = {Banaschewski, Bernhard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {complete lattice; closure operator; fixpoint; frame coproduct; compact frame; fixed point; pre-closure operator; closure system; directed system},
language = {eng},
number = {2},
pages = {303-309},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bourbaki's Fixpoint Lemma reconsidered},
url = {http://eudml.org/doc/247356},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Banaschewski, Bernhard
TI - Bourbaki's Fixpoint Lemma reconsidered
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 303
EP - 309
AB - 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.
LA - eng
KW - complete lattice; closure operator; fixpoint; frame coproduct; compact frame; fixed point; pre-closure operator; closure system; directed system
UR - http://eudml.org/doc/247356
ER -

References

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  1. Banaschewski B., Another look at the localic Tychonoff Theorem, Comment. Math. Univ. Carolinae 29 (1988), 647-656. (1988) Zbl0667.54009MR0982782
  2. Johnstone P.T., Topos Theory, Academic Press, London-New York-San Francisco, 1977. Zbl1071.18002MR0470019
  3. Johnstone P.T., Stone Spaces, Cambridge University Press, 1982. Zbl0586.54001MR0698074
  4. Vermeulen J.J.C., A note on iterative arguments in a topos, preprint, 1990. Zbl0767.18003MR1131478
  5. Vermeulen J.J.C., Some constructive results related to compactness and the (strong) Hausdorff property for locales, preprint, 1991. Zbl0739.18001MR1173026
  6. Witt E., Beweisstudien zum Satz von M. Zorn, Math. Nachr. 4 (1951), 434-438. (1951) Zbl0042.05002MR0039776

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