Quasi-atoms and complete distributivity
HTML articles powered by AMS MathViewer
- by Zi Ke Deng PDF
- Proc. Amer. Math. Soc. 103 (1988), 365-370 Request permission
Abstract:
We introduce quasi-atoms in completely distributive complete lattices and use them to treat the representation of these lattices and their connection with a binary relation.References
- Ph. Dwinger, Characterization of the complete homomorphic images of a completely distributive complete lattice. I, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 4, 403–414. MR 683528
- George N. Raney, Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677–680. MR 52392, DOI 10.1090/S0002-9939-1952-0052392-3
- George N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518–522. MR 58568, DOI 10.1090/S0002-9939-1953-0058568-4
- Garrett Birkhoff, Rings of sets, Duke Math. J. 3 (1937), no. 3, 443–454. MR 1546000, DOI 10.1215/S0012-7094-37-00334-X
- J. C. C. McKinsey and Alfred Tarski, The algebra of topology, Ann. of Math. (2) 45 (1944), 141–191. MR 9842, DOI 10.2307/1969080
- Georg Nöbeling, Grundlagen der analytischen Topologie, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954 (German). MR 0068197 Z. Deng, Neighborhoods in fuzzy topological spaces, J. Hunan Univ. 7 (1980), 1-11.
- J. B. Wright, E. G. Wagner, and J. W. Thatcher, A uniform approach to inductive posets and inductive closure, Theoret. Comput. Sci. 7 (1978), no. 1, 57–77. MR 480224, DOI 10.1016/0304-3975(78)90040-3
- Hans-J. Bandelt and Marcel Erné, The category of $Z$-continuous posets, J. Pure Appl. Algebra 30 (1983), no. 3, 219–226. MR 724033, DOI 10.1016/0022-4049(83)90057-9
- Dan Novak, Generalization of continuous posets, Trans. Amer. Math. Soc. 272 (1982), no. 2, 645–667. MR 662058, DOI 10.1090/S0002-9947-1982-0662058-8
- Jimmie D. Lawson, The duality of continuous posets, Houston J. Math. 5 (1979), no. 3, 357–386. MR 559976
- Rudolf-E. Hoffmann, Continuous posets and adjoint sequences, Semigroup Forum 18 (1979), no. 2, 173–188. MR 540967, DOI 10.1007/BF02574184
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 365-370
- MSC: Primary 06D10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943047-3
- MathSciNet review: 943047