| Title:
|
Remarks on the sobriety of Scott topology and weak topology on posets (English) |
| Author:
|
Wei, He |
| Author:
|
Shouli, Jiang |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
531-535 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4]. (English) |
| Keyword:
|
sober topological space |
| Keyword:
|
Scott topology |
| Keyword:
|
weak topology |
| MSC:
|
06B30 |
| MSC:
|
06B35 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1069.06002 |
| idMR:
|
MR1920529 |
| . |
| Date available:
|
2009-01-08T19:24:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119343 |
| . |
| Reference:
|
[1] Isbell J.R.: Function spaces and adjoints.Math. Scand. 36 (1975), 317-339. Zbl 0309.54016, MR 0405340 |
| Reference:
|
[2] Hoffmann R.-E.: Essentially complete $T_0$ spaces.Manuscripta Math. 27 (1979), 401-432. Zbl 0418.54020, MR 0534803 |
| Reference:
|
[3] Isbell J.R.: Completion of a construction of Johnstone.Proc. Amer. Math. Soc. 85 (1982), 333-334. Zbl 0492.06006, MR 0656096 |
| Reference:
|
[4] Gierz G., Hoffmann K.H., Keimel K., Lawson J.D., Mislove M., Scott D.S.: A Compendium of Continuous Lattices.Springer-Verlag, 1980. MR 0674650 |
| Reference:
|
[5] Johnstone P.T.: Scott is not always sober.Lecture Notes in Math. 871, Springer-Verlag, 1981, pp.282-283. Zbl 0469.06002 |
| . |
