| Title:
|
Samuel compactification and uniform coreflection of nearness $\sigma$-frames (English) |
| Author:
|
Naidoo, Inderasan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1229-1241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the structure of a nearness on a $\sigma $-frame and construct the coreflection of the category ${\mathbf N\sigma Frm}$ of nearness $\sigma $-frames to the category ${\mathbf KReg\sigma Frm}$ of compact regular $\sigma $-frames. This description of the Samuel compactification of a nearness $\sigma $-frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $\sigma $-frames in [11]. We also construct the uniform coreflection of a nearness $\sigma $-frame, that is, the coreflection of the category of ${\mathbf N\sigma Frm}$ to the category U$\sigma $Frm of uniform $\sigma $-frames. (English) |
| Keyword:
|
$\sigma $-frame |
| Keyword:
|
nearness |
| Keyword:
|
Samuel compactification |
| MSC:
|
06D22 |
| MSC:
|
18B35 |
| MSC:
|
54D35 |
| MSC:
|
54E17 |
| idZBL:
|
Zbl 1164.06312 |
| idMR:
|
MR2280806 |
| . |
| Date available:
|
2009-09-24T11:42:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128142 |
| . |
| Reference:
|
[1] D. Baboolal, R. G. Ori: Samuel Compactification and Uniform Coreflection of Nearness Frames. Proc. Symp. on Categorical Topology.University of Cape Town, Cape Town, 1994. MR 1722563 |
| Reference:
|
[2] B. Banaschewski: $\sigma $-Frames.Unpublished manuscript. Zbl 0675.06005 |
| Reference:
|
[3] B. Banaschewski: The frame envelope of a $\sigma $-frame.Quaest. Math. 16 (1993), 51–60. Zbl 0779.06009, MR 1217474 |
| Reference:
|
[4] B. Banaschewski: Completion in pointfree topology.Lecture Notes in Math. and Applied Math, Univ. of Cape Town, SoCat 94, No2/1996. Zbl 1034.06008, MR 1621835 |
| Reference:
|
[5] B. Banaschewski, C. Gilmour: Stone-Čech compactification and dimension theory for regular $\sigma $-frames.J. London Math. Soc. 39 (1989), 1–8. MR 0989914 |
| Reference:
|
[6] B. Banaschewski, A. Pultr: Samuel compactification and completion of uniform frames.Math. Proc. Camb. Phil. Soc. 108 (1990), 63–78. MR 1049760, 10.1017/S030500410006895X |
| Reference:
|
[7] B. Banaschewski, A. Pultr: Cauchy points of uniform and nearness frames.Quaest. Math. 19 (1996), 101–127. MR 1390475, 10.1080/16073606.1996.9631828 |
| Reference:
|
[8] P. T. Johnstone: Stone Spaces. Cambridge Studies in Advanced Math. No. 3.Cambridge University Press, Cambridge, 1982. MR 0698074 |
| Reference:
|
[9] J. J. Madden: $\kappa $-frames.J. Pure Appl. Algebra 70 (1991), 107–127. Zbl 0721.06006, MR 1100510 |
| Reference:
|
[10] I. Naidoo: Nearness and convergence in pointfree topology.PhD. Thesis, University of Cape Town, Cape Town, 2004. |
| Reference:
|
[11] J. L. Walters: Uniform sigma frames and the cozero part of uniform frames.Masters Dissertation, University of Cape Town, Cape Town, 1990. |
| Reference:
|
[12] J. L. Walters: Compactifications and uniformities on $\sigma $-frames.Comm. Math. Univ. Carolinae 32 (1991), 189–198. Zbl 0735.54014, MR 1118301 |
| Reference:
|
[13] J. L. Walters-Wayland: Completeness and nearly fine uniform frames.PhD. Thesis, Univ. Catholique de Louvain, Louvain, 1996. |
| . |
