# Weil uniformities for frames

Commentationes Mathematicae Universitatis Carolinae (1995)

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

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topPicado, 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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