Abstract
The notion of generalized completely distributivity is modified in order to obtain a tractable and consistent property of ordered sets.
This work was supported by the National Natural Science Foundation of China Grant Nos. 11626121 and 11661057, the Ganpo555 programma for leading talents of Jiangxi Province, the NFS of Jiangxi Province Grant Nos. 20161BAB211017 and 20161BAB2061004, the Fund of Education Department of Jiangxi Province Grant No. GJJ150799 and the Young Talent Support Plan of Jiangxi Science and Technology Normal University No. 2016QNBJRC008.
References
[1] Banaschwski, P.—Ebrahimi, M. M.—Mahmoudi, M.: On the normal completion of a Boolean algebra, J. Pure Appl. Algebra 181 (2003), 1–14.10.1016/S0022-4049(02)00290-6Suche in Google Scholar
[2] Crawley, P.—Dilworth, R. P.: Algebraic Theory of Lattices, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973.Suche in Google Scholar
[3] Dedekind, R.: Stetigkeit und Irrationale Zahlen, Vieweg, Braunschweig, 1872.Suche in Google Scholar
[4] Erné, M.: A completion-invariant extension of the concept of continuous lattices. In: Continuous Lattices (B. Banaschewski and R.-E. Hoffmann, eds.), Proc. Bremen 1979. Lecture Notes in Math. 871, Springer-Verlag, Berhn-Heidelberg-New York, 1981, pp. 43–60.10.1007/BFb0089903Suche in Google Scholar
[5] Erné, M.: The Dedekind-MacNeille completion as a reflector, Order 8 (1991), 159–173.10.1007/BF00383401Suche in Google Scholar
[6] Erné, M.: Bigeneration in complete lattices and principal separation in partially ordered sets, Order 8 (1991), 197–221.10.1007/BF00383404Suche in Google Scholar
[7] Frink, O.: Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954), 223–234.10.2307/2306387Suche in Google Scholar
[8] Gierz, G.—Lawson, J. D.: Generalized continuous lattices and hypercontinuous lattices, Rocky Mountain J. Math. 11 (1981), 271–296.10.1216/RMJ-1981-11-2-271Suche in Google Scholar
[9] Gierz, G.—Hofmann, K.—Keimel, K.—Lawson, J. D.—Mislove, M.—Scott, D.: Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.10.1017/CBO9780511542725Suche in Google Scholar
[10] Herrlich, H.—Strecker, G.: Category Theory, Heldermann Verlag, Berlin, 1979.Suche in Google Scholar
[11] Harding, J.—Bezhanishvili, G.: Macneille completions of Heyting algebras, Houston J. Math. 30 (2004), 937–952.10.1007/s11225-021-09941-6Suche in Google Scholar
[12] MacNeille, H. M.: Partially ordered sets, Trans Amer. Math. Soc. 42 (1937), 416–460.10.1090/S0002-9947-1937-1501929-XSuche in Google Scholar
[13] Niederle, J.: Boolean and distributive ordered sets: Characterization and representation by sets, Order 12 (1995), 189–210.10.1007/BF01108627Suche in Google Scholar
[14] Niederle, J.: On infinitely distributive ordered sets, Math. Slovaca 55 (2005), 495–502.Suche in Google Scholar
[15] Raney, G.: A subdirect union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518–522.10.1090/S0002-9939-1953-0058568-4Suche in Google Scholar
[16] Venugopolan, P.: A generalization of completely disdributive lattices, Algebra Universalis 27 (1990), 578–586.10.1007/BF01189001Suche in Google Scholar
[17] Yang, J. B.—Xu, X. Q.: The dual of a generalized completely distributive lattice is a hypercontinuous lattice, Algebra Universalis 63 (2010), 275–281.10.1007/s00012-010-0078-zSuche in Google Scholar
[18] Yang, J. B.—Luo, M. K.: Quasicontinuous domains and generalized completely distributive lattices, Adv. Math. (China) 36 (2007), 399–406.Suche in Google Scholar
[19] Zhang, W. F.—Xu, X. Q.: Completely precontinuous posets, Electron. Notes Theor. Comput. Sci. 301 (2014), 169–178.10.1016/j.entcs.2014.01.014Suche in Google Scholar
[20] Zhang, W. F.—Xu, X. Q.: Meet precontinuous posets, Electron. Notes Theor. Comput. Sci. 301 (2014), 179-188.10.1016/j.entcs.2014.01.015Suche in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- Cyclic and rotational latin hybrid triple systems
- Notes on mildly distributive semilattices
- On generalized completely distributive posets
- Properties of non-associative MV-algebras
- On the upper and lower exponential density functions
- Quadratic permutations, complete mappings and mutually orthogonal latin squares
- On F-groups with the central factor of order p4
- Comparison of some families of real functions in porosity terms
- Negative interest rates: why and how?
- Homoclinic and heteroclinic motions in hybrid systems with impacts
- Some fixed point theorems in Branciari metric spaces
- S-essential spectra and measure of noncompactness
- Unified approach to graphs and metric spaces
- On structural properties of porouscontinuous functions
- A class of topological spaces between the classes of regular and urysohn spaces
- On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
- Generalized Baskakov type operators