Completeness and Compact Generation in Partially Ordered Sets
- Department of Mathematics, University of Mazandaran, P. O. Box 95447, Babolsar, Iran.
- Department of Mathematics, University of Pune, Pune 411007, India.
In this paper we introduce a notion of density in posets in a more general fashion. We also
introduce completeness in posets and study compact generation in posets based on such completeness
Share and Cite
A. Vaezi, V. Kharat, Completeness and Compact Generation in Partially Ordered Sets, Journal of Mathematics and Computer Science, 16 (2016), no. 1, 69-76
Vaezi A., Kharat V., Completeness and Compact Generation in Partially Ordered Sets. J Math Comput SCI-JM. (2016); 16(1):69-76
Vaezi, A., Kharat, V.. "Completeness and Compact Generation in Partially Ordered Sets." Journal of Mathematics and Computer Science, 16, no. 1 (2016): 69-76
- U-complete poset
- U-compactly generated poset
- U-regular interval.
G. Birkhoff, Lattice Theory, American Mathematical Society, New York (1940)
A. Björner, On complements in lattices of finite length, Discrete Math., 36 (1981), 325-326.
I. Chajda, Complemented ordered sets, Arch. Math. (Brno), 28 (1992), 25-34.
I. Chajda, Z. Morávková, Relatively complemented ordered sets, Discuss. Math. Gen. Algebra Appl., 20 (2000), 207-217.
P. Crawley, R. P. Dilworth, Algebraic Theory of Lattices, Prentice- Hall, Englewood Cliffs, (1973), 1015-1023.
M. Erné, Compact generation in partially ordered sets, J. Austral. Math. Soc. Ser. A, 42 (1987), 69-83.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, D. S. Scott, A Compendium of Continuous Lattices, Springer-Verlag, Berlin-New York (1980)
J. A. Kalman, A property of algebraic lattices whose compact elements have complements, Algebra Universalis, 22 (1986), 100-101.
R. S. Shewale, Modular pairs, forbidden configurations and related aspects in partially ordered sets, Ph. D. Thesis, University of Pune, Pune (INDIA) (2010)
M. Stern, Semimodular lattices: Theory and Applications, Cambridge University Press, Cambridge (1999)