Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
completely distributive lattice; interval topology; AR; ANR
completely distributive lattice; interval topology; AR; ANR
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.
References:
[1] Engelking R.: General Topology. PWN, 1977. MR 0500780 | Zbl 0684.54001
[2] Gierz G. et al.: A Compendium of Continuous Lattices. Springer-Verlag, 1980. MR 0614752 | Zbl 0452.06001
[3] van Gool F.: Lower semicontinuous functions with values in a continuous lattice. Comment. Math. Univ. Carolinae 33 (1992), 505-523. MR 1209292 | Zbl 0769.06005
[4] Hu S.T.: Theory of Retracts. Wayne State University Press, 1965. MR 0181977 | Zbl 1164.54341
[5] Johnstone P.T.: Stone Spaces. Cambridge University Press, 1982. MR 0698074 | Zbl 0586.54001
[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
[7] Liu Ying-Ming et al.: Topological and analytic characterizations of completely distributive law. Sci. Bull. 35 (1990), 1223-1226.
[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
[9] Steen L.A., Seebach J.A., Jr.: Counterexamples in topology. second edition, Springer-Verlag, 1978. MR 0507446 | Zbl 0386.54001
[10] Tong H.: Some characterizations of normal and perfectly normal spaces. Duke Math. J. 19 (1952), 289-292. MR 0050265 | Zbl 0046.16203
[11] Xu Luo-Shan: Research on lattice and topology. PhD. Dissertation of Sichuan University, 1992.
[12] Zhang De-Xue: Continuous lattices and spaces of semicontinuous functions. preprint.
Search
Partner of
