Metrizable completely distributive lattices
De-Xue, Zhang
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 137-148 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1997-01-01
Classification:  06B30,  06B35,  06D10,  54C08,  54C15,  54C55,  54E35,  54H12 
@article{118909,
     author = {Zhang De-Xue},
     title = {Metrizable completely distributive lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {137-148},
     zbl = {0887.06006},
     mrnumber = {1455477},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118909}
}

De-Xue, Zhang. Metrizable completely distributive lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 137-148. http://gdmltest.u-ga.fr/item/118909/

Engelking R. General Topology, PWN, 1977. | MR 0500780 | Zbl 0684.54001

Gierz G. Et Al. A Compendium of Continuous Lattices, Springer-Verlag, 1980. | MR 0614752 | Zbl 0452.06001

Van Gool F. Lower semicontinuous functions with values in a continuous lattice, Comment. Math. Univ. Carolinae 33 (1992), 505-523. (1992) | MR 1209292 | Zbl 0769.06005

Hu S.T. Theory of Retracts, Wayne State University Press, 1965. | MR 0181977 | Zbl 1164.54341

Johnstone P.T. Stone Spaces, Cambridge University Press, 1982. | MR 0698074 | Zbl 0586.54001

Katětov M. On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91 Correction in Fund. Math. 40 (1953), 203-205. (1953) | MR 0050264

Liu Ying-Ming Et Al. Topological and analytic characterizations of completely distributive law, Sci. Bull. 35 (1990), 1223-1226. (1990)

Liu Ying-Ming; Luo Mao-Kang Lattice-valued Hahn-Diedonne-Tong insertion theorem and stratification structure, Topology Appl. 45 (1992), 173-188. (1992) | MR 1180808

Steen L.A.; Seebach J.A., Jr. Counterexamples in topology, second edition, Springer-Verlag, 1978. | MR 0507446 | Zbl 0386.54001

Tong H. Some characterizations of normal and perfectly normal spaces, Duke Math. J. 19 (1952), 289-292. (1952) | MR 0050265 | Zbl 0046.16203

Xu Luo-Shan Research on lattice and topology, PhD. Dissertation of Sichuan University, 1992.

Zhang De-Xue Continuous lattices and spaces of semicontinuous functions, preprint.