| Title:
|
Metrizable completely distributive lattices (English) |
| Author:
|
De-Xue, Zhang |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
137-148 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements. (English) |
| Keyword:
|
completely distributive lattice |
| Keyword:
|
interval topology |
| Keyword:
|
AR |
| Keyword:
|
ANR |
| MSC:
|
06B30 |
| MSC:
|
06B35 |
| MSC:
|
06D10 |
| MSC:
|
54C08 |
| MSC:
|
54C15 |
| MSC:
|
54C55 |
| MSC:
|
54E35 |
| MSC:
|
54H12 |
| idZBL:
|
Zbl 0887.06006 |
| idMR:
|
MR1455477 |
| . |
| Date available:
|
2009-01-08T18:29:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118909 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.PWN, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[2] Gierz G. et al.: A Compendium of Continuous Lattices.Springer-Verlag, 1980. Zbl 0452.06001, MR 0614752 |
| Reference:
|
[3] van Gool F.: Lower semicontinuous functions with values in a continuous lattice.Comment. Math. Univ. Carolinae 33 (1992), 505-523. Zbl 0769.06005, MR 1209292 |
| Reference:
|
[4] Hu S.T.: Theory of Retracts.Wayne State University Press, 1965. Zbl 1164.54341, MR 0181977 |
| Reference:
|
[5] Johnstone P.T.: Stone Spaces.Cambridge University Press, 1982. Zbl 0586.54001, MR 0698074 |
| Reference:
|
[6] Katětov M.: On real-valued functions in topological spaces.Fund. Math. 38 (1951), 85-91 Correction in Fund. Math. 40 (1953), 203-205. MR 0050264 |
| Reference:
|
[7] Liu Ying-Ming et al.: Topological and analytic characterizations of completely distributive law.Sci. Bull. 35 (1990), 1223-1226. |
| Reference:
|
[8] Liu Ying-Ming, Luo Mao-Kang: Lattice-valued Hahn-Diedonne-Tong insertion theorem and stratification structure.Topology Appl. 45 (1992), 173-188. MR 1180808 |
| Reference:
|
[9] Steen L.A., Seebach J.A., Jr.: Counterexamples in topology.second edition, Springer-Verlag, 1978. Zbl 0386.54001, MR 0507446 |
| Reference:
|
[10] Tong H.: Some characterizations of normal and perfectly normal spaces.Duke Math. J. 19 (1952), 289-292. Zbl 0046.16203, MR 0050265 |
| Reference:
|
[11] Xu Luo-Shan: Research on lattice and topology.PhD. Dissertation of Sichuan University, 1992. |
| Reference:
|
[12] Zhang De-Xue: Continuous lattices and spaces of semicontinuous functions.preprint. |
| . |
