- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 942628, 8 pages
Some New Intrinsic Topologies on Complete Lattices and the Cartesian Closedness of the Category of Strongly Continuous Lattices
1Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha 410004, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
3Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walt, Singapore 637616
Received 2 December 2012; Accepted 20 January 2013
Academic Editor: Turgut Öziş
Copyright © 2013 Xiuhua Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. Scott, “Continuous Lattices,” in Toposes, Algebraic Geometry and Logic (Conf., Dalhousie Univ., Halifax, N. S., 1971), vol. 274 of Lecture Notes in Math., pp. 97–136, Springer, Berlin, Germany, 1972.
- G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, Continuous Lattices and Domains, Springer, Berlin, Germany, 2003.
- A. Jung, “Cartesian closed categories of algebraic cpos,” Theoretical Computer Science, vol. 70, no. 2, pp. 233–250, 1990.
- G. Gierz and J. D. Lawson, “Generalized continuous and hypercontinuous lattices,” The Rocky Mountain Journal of Mathematics, vol. 11, no. 2, pp. 271–296, 1981.
- D. Zhao, “Semicontinuous lattices,” Algebra Universalis, vol. 37, no. 4, pp. 458–476, 1997.
- R. C. Powers and T. Riedel, “-semicontinuous posets,” Order, vol. 20, no. 4, pp. 365–371, 2003.
- Y. Liu and L. Xie, “On the category of semicontinuous lattices,” Journal of Liaoning Normal University (Natural Science), vol. 20, no. 3, pp. 182–185, 1997 (Chinese).
- Y. Liu and L. Xie, “On the structure of semicontinuous lattices and cartesian closedness of categories of semicontinuous lattices,” Journal of Liaoning Normal University (Natural Science), vol. 18, no. 4, pp. 265–268, 1995 (Chinese).
- X. H. Wu, Q. G. Li, and R. F. Xu, “Some properties of semicontinuous lattices,” Fuzzy Systems and Mathematics, vol. 20, no. 4, pp. 42–46, 2006 (Chinese).
- X. H. Wu and Q. G. Li, “Characterizations and functions of semicontinuous lattices,” Journal of Mathematical Research and Exposition, vol. 27, no. 3, pp. 654–658, 2007 (Chinese).
- Y. Rav, “Semiprime ideals in general lattices,” Journal of Pure and Applied Algebra, vol. 56, no. 2, pp. 105–118, 1989.
- G. N. Raney, “Completely distributive complete lattices,” Proceedings of the American Mathematical Society, vol. 3, pp. 677–680, 1952.
- B. Zhao and D. Zhao, “Lim-inf convergence in partially ordered sets,” Journal of Mathematical Analysis and Applications, vol. 309, no. 2, pp. 701–708, 2005.
- M. B. Smyth, “The largest Cartesian closed category of domains,” Theoretical Computer Science, vol. 27, no. 1-2, pp. 109–119, 1983.