| Title:
|
Weil uniformities for frames (English) |
| Author:
|
Picado, Jorge |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
357-370 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
uniform space |
| Keyword:
|
frame |
| Keyword:
|
uniform frame |
| Keyword:
|
uniform frame homomorphism |
| Keyword:
|
$C$-ideal |
| Keyword:
|
frame coproduct |
| Keyword:
|
entourage |
| Keyword:
|
Weil uniform frame |
| Keyword:
|
Weil homomorphism |
| MSC:
|
06D20 |
| MSC:
|
54E15 |
| MSC:
|
54E55 |
| idZBL:
|
Zbl 0832.54025 |
| idMR:
|
MR1357535 |
| . |
| Date available:
|
2009-01-08T18:18:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118762 |
| . |
| Reference:
|
[1] Banaschewski B.: Another look at the localic Tychonoff Theorem.Comment. Math. Univ. Carolinae 29 (1988), 647-656. Zbl 0667.54009, MR 0982782 |
| Reference:
|
[2] Banaschewski B.: Bourbaki's Fixpoint Lemma reconsidered.Comment. Math. Univ. Carolinae 33 (1992), 303-309. Zbl 0779.06004, MR 1189661 |
| Reference:
|
[3] Banaschewski B., Brümmer G.C.L., Hardie K.A.: Biframes and bispaces.Quaestiones Math. 6 (1983), 13-25. MR 0700237 |
| Reference:
|
[4] Bourbaki N.: Topologie générale.Hermann, Paris, 1982. Zbl 1107.54001 |
| Reference:
|
[5] Dowker C.H., Strauss D.: Sums in the category of frames.Houston J. Math. 3 (1977), 7-15. Zbl 0341.54001, MR 0442900 |
| Reference:
|
[6] Fletcher P., Hunsaker W.: Entourage uniformities for frames.Monatsh. Math. 112 (1991), 271-279. Zbl 0736.54023, MR 1141095 |
| Reference:
|
[7] Fletcher P., Hunsaker W., Lindgren W.: Characterizations of frame quasi-uniformities.Quaestiones Math. 16 (1993), 371-383. Zbl 0792.54026, MR 1254164 |
| Reference:
|
[8] Fletcher P., Hunsaker W., Lindgren W.: Totally bounded frame quasi-uniformities.Comment. Math. Univ. Carolinae 34 (1993), 529-537. Zbl 0786.54028, MR 1243084 |
| Reference:
|
[9] Fletcher P., Hunsaker W., Lindgren W.: Frame quasi-uniformities.Monatsh. Math. 117 (1994), 223-236. Zbl 0796.54037, MR 1279114 |
| Reference:
|
[10] Frith J.L.: Structured frames.PhD Thesis, University of Cape Town, 1987. |
| Reference:
|
[11] Isbell J.: Atomless parts of spaces.Math. Scand. 31 (1972), 5-32. Zbl 0246.54028, MR 0358725 |
| Reference:
|
[12] Johnstone P.T.: Stone spaces.Cambridge Studies in Advanced Mathematics 3, Cambridge University Press, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[13] Picado J.: Frame quasi-uniformities by entourages.preprint (Universidade de Coimbra, 1994). Zbl 1005.54030, MR 1722578 |
| Reference:
|
[14] Pultr A.: Pointless uniformities I. Complete regularity.Comment. Math. Univ. Carolinae 25 (1984), 91-104. Zbl 0543.54023, MR 0749118 |
| Reference:
|
[15] Pultr A.: Pointless uniformities II. (Dia)metrization.Comment. Math. Univ. Carolinae 25 (1984), 105-120. MR 0749119 |
| Reference:
|
[16] Tukey J.W.: Convergence and uniformity in topology.Ann. of Math. Studies 2, Princeton University Press, 1940. Zbl 0025.09102, MR 0002515 |
| Reference:
|
[17] Weil A.: Sur les espaces à structure uniforme et sur la topologie générale.Hermann, Paris, 1938. Zbl 0019.18604 |
| . |
