GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

doi:10.1016/S0252-9602(09)60109-0

Abstract

Abstract:

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also
semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

Key words: semicontinuous lattices, strongly semicontinuous lattices, semicontinuous mapping, hereditary, function space, Cartesian closed category

CLC Number:

06A15

LI Qiang-Guo, WU Xiu-Hua. GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES[J].Acta mathematica scientia,Series B, 2009, 29(5): 1366-1374.

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References

[1] Novak D. Generalization of continuous posets. Trans Amer Math Soc, 1982, 272(2): 645--667

[2] Gierz G, Lawson J D, Stralka A. Quasicontinuous posets. Houston J Math, 1983, 9: 191--208

[3] Venugopalan P. Z-continuous posets. Houston J Math, 1986, 12(2): 275--294

[4] Baranga A. Z-continuous posets. Discrete Math, 1996, 152: 33--45

[5] Zhao D S. Semicontinuous lattices. Algebra Universalis, 1997, 37: 458--476

[6] Powers R C, Riedel T. Z-semicontinuous posets. Order, 2003, 20: 365--371

[7] Gierz G etal. Continuous Lattices and Domains. London: Cambridge University Press, 2003

[8] Ray Y. Semiprime ideals in general lattices. J Pure Appl Algebra, 1989, 56: 105--118

[9] Wright J B, Wagner E G, Thatcher J W. A uniform approach to inductive posets and inductive closure. Theoret
Comput Sci, 1978, 7: 55--77

[10] Zhao D S, Zhao B. Generalization of Lawson Hoffmann duality. Acta Mathematica Sinica, 1998, 41(6): 1325--1332 (in Chinese)

[11] Wu X H, Li Q G. Characterizations and functions of semicontinuous lattices. J Math Research and Exposition, 2007, 27(3): 654--658 (in Chinese)

[12] Smyth M. The largest Cartesian closed category of domains. Theoret Comput Sci, 1983, 27: 109--119

[13] Liu Y M, Liang J H. Solutions to two problems of J. D. Lawson and M. Mislove. Topology Appl, 1996, 69: 153--164

[14] Thomas E, Martin H E, Klaus K. The way-below relation of function spaces over semantic domains. Topology Appl, 1998, 89: 61--74

[15] Chen X T, Li Q G, Long F, Deng Z K. Tietze extension theorem on additive generalized algebraic lattice.
Acta Mathematica Scientia, 2007, 27A(1): 104--110 (in Chinese)

[16] Li Q G, Chen X T, Cai H T. A sufficient and necessary condition for quasi-proximatable of algebra of bitopology. Acta Mathematica Scientia, 2006, 26A(5): 721--724 (in Chinese)