Title:
|
Metric-fine uniform frames (English) |
Author:
|
Walters-Wayland, J. L. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
39 |
Issue:
|
3 |
Year:
|
1998 |
Pages:
|
617-632 |
. |
Category:
|
math |
. |
Summary:
|
A locallic version of Hager's metric-fine spaces is presented. A general definition of $\Cal A$-fineness is given and various special cases are considered, notably $\Cal A =$ all metric frames, $\Cal A =$ complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed. (English) |
Keyword:
|
uniform frames and sigma frames |
Keyword:
|
fine |
Keyword:
|
metric-fine |
Keyword:
|
completion |
MSC:
|
06A23 |
MSC:
|
06B99 |
MSC:
|
54A05 |
MSC:
|
54D20 |
MSC:
|
54D30 |
MSC:
|
54E15 |
idZBL:
|
Zbl 0962.54021 |
idMR:
|
MR1666802 |
. |
Date available:
|
2009-01-08T18:46:59Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119038 |
. |
Reference:
|
[1] Banaschewski B.: Recent results in pointfree topology.Annals New York Acad. of Sci. 659 (1992), 29-41. MR 1485267 |
Reference:
|
[2] Banaschewski B.: The frame envelope of a $\sigma $-frame.Quaestiones Math. 16 (1991), 51-60. MR 1217474 |
Reference:
|
[3] Banaschewski B., Gilmour C.R.A.: Stone Čech compactification and dimension theory for regular $\sigma$-frames.J. London Math. Soc. 39 (1989), 1-8. Zbl 0675.06005, MR 0989914 |
Reference:
|
[4] Banaschewski B., Gilmour C.R.A.: Pseudocompactness and the cozero part of a frame.Comment. Math. Univ. Carolinae 37 (1996), 577-587. Zbl 0881.54018, MR 1426922 |
Reference:
|
[5] Banaschewski B., Mulvey C.: Stone Čech compactification of locales I.Houston J. Math. 6 (1980), 301-312. Zbl 0473.54026, MR 0597771 |
Reference:
|
[6] Banaschewski B., Pultr A.: Samuel compactification and completion of uniform frames.Math. Proc. Camb. Phil. Soc. 108 (1990), 63-78. Zbl 0733.54020, MR 1049760 |
Reference:
|
[7] Banaschewski B., Pultr A.: Paracompactness revisited.Applied Categorical Structures 1 (1993), 181-190. Zbl 0797.54032, MR 1245799 |
Reference:
|
[8] Gillman L., Jerrison M.: Rings of Continuous Functions.Van Nostrand Princeton (1960). MR 0116199 |
Reference:
|
[9] Gilmour C.R.A.: Realcompact Alexandroff spaces and regular $\sigma$-frames.Math. Proc. Camb. Phil. Soc. 96 (1984), 73-79. MR 0743702 |
Reference:
|
[10] Frolik Z.: A note on metric-fine spaces.Proc. Amer. Math. Soc. 46 (1974), 111-119. Zbl 0301.54033, MR 0358704 |
Reference:
|
[11] Hager A.: Some nearly fine uniform spaces.Proc. London Math. Soc. 28 (1974), 517-546. Zbl 0284.54017, MR 0397670 |
Reference:
|
[12] Hager A.: Three classes of uniform spaces.Proc. Prague Conf. on General Topology, 1971. Zbl 0313.54030, MR 0353270 |
Reference:
|
[13] Hager A.: Uniformities induced by proximity, cozero and Baire sets..unpublished manuscript. |
Reference:
|
[14] Hager A., Rice M.D.: Coreflections commuting with completion.J. of Math. 26 (101) (1976), 371-380. MR 0418051 |
Reference:
|
[15] Isbell J.: Atomless parts of spaces.Math. Scand. 31 (1972), 5-32. Zbl 0246.54028, MR 0358725 |
Reference:
|
[16] Isbell J.: Uniform Spaces.Amer. Math. Soc. Providence (1964). Zbl 0124.15601 |
Reference:
|
[17] Johnstone P.T.: Stone Spaces.Cambridge Studies in Advanced Math. Cambridge University Press (1982). Zbl 0499.54001, MR 0698074 |
Reference:
|
[18] Johnstone P.T.: The point of pointless topology.Bull. Amer. Math. Soc 8 (1983), 41-52. Zbl 0499.54002, MR 0682820 |
Reference:
|
[19] Kříž I.: A direct description of uniform completion in locales and a characterization of LT groups.Cahiers Topologie et Geom. Differentielle Categoriques 27 (1986), 19-34. MR 0845407 |
Reference:
|
[20] Kříž I., Pultr A.: Systems of covers of frames and resulting subframes.Proc. 14th Winter School, Suppl. ai Rendiconti del Circ. Mat. di Palermo 14 (1987), 353-364. MR 0920868 |
Reference:
|
[21] Madden J.: Kappa frames.J. Pure and Applied Algebra 70 (1991), 107-127. Zbl 0721.06006, MR 1100510 |
Reference:
|
[22] Madden J., Vermeer H.: Lindelöf locales and realcompactness.Math. Proc. Camb. Phil. Soc. 99 (1986), 473-480. Zbl 0603.54021, MR 0830360 |
Reference:
|
[23] Pultr A.: Pointless uniformities I: Complete regularity.Comment. Math. Univ. Carolinae 25 (1984), 91-104. Zbl 0543.54023, MR 0749118 |
Reference:
|
[24] Pultr A.: Pointless uniformities II: (Dia)metrization.Comment. Math. Univ. Carolinae 25 (1984), 104-120. MR 0749119 |
Reference:
|
[25] Pultr A.: Remarks on metrizable frames.Proc. 12th Winter School, Suppl. ai Rendiconti del Circ. Mat. di Palermo 6 (1984), 247-258. MR 0782722 |
Reference:
|
[26] Pultr A., Ulehla J.: Notes on characterization of paracompact frames.Comment. Math. Univ. Carolinae 30 (1989), 377-384. Zbl 0672.54018, MR 1014137 |
Reference:
|
[27] Reynolds G.: Alexandroff algebras and complete regularity.Proc. Amer. Math. Soc. 76 (1979), 322-326. Zbl 0416.54015, MR 0537098 |
Reference:
|
[28] Rice M.D.: Metric-fine uniform spaces.Proc. London Math. Soc. 11 (1975), 53-64. Zbl 0324.54018, MR 0420566 |
Reference:
|
[29] Rice M.D.: Complete uniform spaces.Proc. Second Internat. Topology Conf. (Pittsburgh), 1972. Zbl 0327.54025 |
Reference:
|
[30] Rice M.D.: Subcategories of uniform spaces.Trans. Amer. Math. Soc. 221 (1975), 305-314. Zbl 0306.54038, MR 0358708 |
Reference:
|
[31] Sun S.H.: On paracompact locales and metric locales.Comment. Math. Univ. Carolinae 30 (1989), 101-107. Zbl 0691.06003, MR 0995708 |
Reference:
|
[32] Walters J.L.: Uniform sigma frames and the cozero part of uniform frames.Masters Thesis, University of Cape Town (1989). |
Reference:
|
[33] Walters J.L.: Compactifications and uniformities on sigma frames.Comm. Math. Univ. Carolinae 32 (1991), 189-198. Zbl 0735.54014, MR 1118301 |
Reference:
|
[34] Walters-Wayland J.L.: Completeness and nearly fine uniform frames.Doctoral Thesis, Universite Catholique de Louvain (1995). |
Reference:
|
[35] Walters-Wayland J.L.: Shirota's Theorem in the frame setting.preprint. |
Reference:
|
[36] Walters-Wayland J.L.: Cozfine and measurable uniform frames.preprint. Zbl 0935.54004, MR 1733252 |
Reference:
|
[37] Walters-Wayland J.L.: Injectivity and subfineness in uniform locales.preprint. |
Reference:
|
[38] Willard S.: General Topology.Addison-Wesley Reading, Mass. (1970). Zbl 0205.26601, MR 0264581 |
. |