Weil uniformities for frames

Jorge Picado

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 357-370
  • ISSN: 0010-2628

Abstract

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In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed in terms of products of locales. We show that our definition is equivalent to the previous ones by proving that our category of Weil uniform frames is isomorphic to the one defined in [6].

How to cite

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Picado, Jorge. "Weil uniformities for frames." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 357-370. <http://eudml.org/doc/247721>.

@article{Picado1995,
abstract = {In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed in terms of products of locales. We show that our definition is equivalent to the previous ones by proving that our category of Weil uniform frames is isomorphic to the one defined in [6].},
author = {Picado, Jorge},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {uniform space; frame; uniform frame; uniform frame homomorphism; $C$-ideal; frame coproduct; entourage; Weil uniform frame; Weil homomorphism; entourage; uniform frame; locale},
language = {eng},
number = {2},
pages = {357-370},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Weil uniformities for frames},
url = {http://eudml.org/doc/247721},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Picado, Jorge
TI - Weil uniformities for frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 357
EP - 370
AB - In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed in terms of products of locales. We show that our definition is equivalent to the previous ones by proving that our category of Weil uniform frames is isomorphic to the one defined in [6].
LA - eng
KW - uniform space; frame; uniform frame; uniform frame homomorphism; $C$-ideal; frame coproduct; entourage; Weil uniform frame; Weil homomorphism; entourage; uniform frame; locale
UR - http://eudml.org/doc/247721
ER -

References

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  6. Fletcher P., Hunsaker W., Entourage uniformities for frames, Monatsh. Math. 112 (1991), 271-279. (1991) Zbl0736.54023MR1141095
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  8. Fletcher P., Hunsaker W., Lindgren W., Totally bounded frame quasi-uniformities, Comment. Math. Univ. Carolinae 34 (1993), 529-537. (1993) Zbl0786.54028MR1243084
  9. Fletcher P., Hunsaker W., Lindgren W., Frame quasi-uniformities, Monatsh. Math. 117 (1994), 223-236. (1994) Zbl0796.54037MR1279114
  10. Frith J.L., Structured frames, PhD Thesis, University of Cape Town, 1987. 
  11. Isbell J., Atomless parts of spaces, Math. Scand. 31 (1972), 5-32. (1972) Zbl0246.54028MR0358725
  12. Johnstone P.T., Stone spaces, Cambridge Studies in Advanced Mathematics 3, Cambridge University Press, 1982. Zbl0586.54001MR0698074
  13. Picado J., Frame quasi-uniformities by entourages, preprint (Universidade de Coimbra, 1994). Zbl1005.54030MR1722578
  14. Pultr A., Pointless uniformities I. Complete regularity, Comment. Math. Univ. Carolinae 25 (1984), 91-104. (1984) Zbl0543.54023MR0749118
  15. Pultr A., Pointless uniformities II. (Dia)metrization, Comment. Math. Univ. Carolinae 25 (1984), 105-120. (1984) MR0749119
  16. Tukey J.W., Convergence and uniformity in topology, Ann. of Math. Studies 2, Princeton University Press, 1940. Zbl0025.09102MR0002515
  17. Weil A., Sur les espaces à structure uniforme et sur la topologie générale, Hermann, Paris, 1938. Zbl0019.18604

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