| Title:
|
A new look at pointfree metrization theorems (English) |
| Author:
|
Banaschewski, B. |
| Author:
|
Pultr, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
167-175 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context. (English) |
| Keyword:
|
frame |
| Keyword:
|
(metric) diameter |
| Keyword:
|
metrization |
| MSC:
|
06A23 |
| MSC:
|
06D10 |
| MSC:
|
06D20 |
| MSC:
|
06D22 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 0937.54019 |
| idMR:
|
MR1623010 |
| . |
| Date available:
|
2009-01-08T18:39:49Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118995 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/119020 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.Sigma Series in Pure Mathematics, Vol.6, Helderman Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[2] Isbell J.R.: Atomless parts of spaces.Math. Scand. 31 (1972), 5-32. Zbl 0246.54028, MR 0358725 |
| Reference:
|
[3] Isbell J.R.: Graduation and dimension in locales.in: Aspects of Topology, London MS Lecture Notes 93 (1985), 195-210. Zbl 0555.54020, MR 0787829 |
| Reference:
|
[4] Johnstone P.T.: Stone Spaces.Cambridge University Press, Cambridge, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[5] Kaiser T.: A sufficient condition of full normality.Comment Math. Univ. Carolinae 37 (1996), 381-389. Zbl 0847.54025, MR 1399010 |
| Reference:
|
[6] Pultr A.: Pointless uniformities II. (Dia)metrization.Comment. Math. Univ. Carolinae 25 (1984), 105-120. MR 0749119 |
| Reference:
|
[7] Pultr A.: Remarks on metrizable locales.Suppl. Rend. Circ. Mat. Palermo 6 (1984), 247-258. Zbl 0565.54001, MR 0782722 |
| Reference:
|
[8] Pultr A.: Diameters in locales: How bad they can be.Comment. Math. Univ. Carolinae 29 (1988), 731-742. Zbl 0668.06008, MR 0982793 |
| Reference:
|
[9] Pultr A., Úlehla J.: Notes on characterization of paracompact frames.Comment. Math. Univ. Carolinae 30 (1989), 377-384. MR 1014137 |
| Reference:
|
[10] Sun Shu-Hao: On paracompact locales and metric locales.Comment. Math. Univ. Carolinae 30 (1989), 101-107. MR 0995708 |
| Reference:
|
[11] Vickers S.: Topology via Logic.Cambridge Tracts in Theor. Comp. Sci., Number 5, Cambridge University Press, Cambridge, 1985. Zbl 0922.54002, MR 1002193 |
| . |
