Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 328153, 11 pages
http://dx.doi.org/10.1155/2014/328153
Research Article

Lattice-Valued Convergence Spaces: Weaker Regularity and -Regularity

1Department of Mathematics, Liaocheng University, Liaocheng 252059, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 5 September 2013; Accepted 7 December 2013; Published 12 January 2014

Academic Editor: Abdelghani Bellouquid

Copyright © 2014 Lingqiang Li and Qiu Jin. 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.

Linked References

  1. H. J. Kowalsky, “Limesräume und Komplettierung,” Mathematische Nachrichten, vol. 12, pp. 301–340, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. C. H. Cook and H. R. Fischer, “Regular convergence spaces,” Mathematische Annalen, vol. 174, no. 1, pp. 1–7, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. D. C. Kent and G. D. Richardson, “p-regular convergence spaces,” Mathematische Nachrichten, vol. 149, pp. 215–222, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. A. Wilde and D. C. Kent, “p-topological and p-regular: dual notions in convergence theory,” International Journal of Mathematics and Mathematical Sciences, vol. 22, pp. 1–12, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. W. Gähler, “Monadic topology—a new concept of generalized topology,” in Recent Developments of General Topology, vol. 67 of Mathematical Research, pp. 136–149, Akademie, Berlin, Germany, 1992. View at Google Scholar · View at Zentralblatt MATH
  6. D. C. Kent and G. D. Richardson, “Convergence spaces and diagonal conditions,” Topology and its Applications, vol. 70, no. 2-3, pp. 167–174, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. G. Jäger, “A category of L-fuzzy convergence spaces,” Quaestiones Mathematicae, vol. 24, pp. 501–517, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. M. Fang, “Stratified L-ordered convergence structures,” Fuzzy Sets and Systems, vol. 161, no. 16, pp. 2130–2149, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. J. M. Fang, “Relationships between L-ordered convergence structures and strong L-topologies,” Fuzzy Sets and Systems, vol. 161, no. 22, pp. 2923–2944, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. G. Jäger, “Subcategories of lattice-valued convergence spaces,” Fuzzy Sets and Systems, vol. 156, no. 1, pp. 1–24, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. G. Jäger, “Pretopological and topological lattice-valued convergence spaces,” Fuzzy Sets and Systems, vol. 158, no. 4, pp. 424–435, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. G. Jäger, “Fischer's diagonal condition for lattice-valued convergence spaces,” Quaestiones Mathematicae, vol. 31, no. 1, pp. 11–25, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. G. Jäger, “Lattice-valued convergence spaces and regularity,” Fuzzy Sets and Systems, vol. 159, no. 19, pp. 2488–2502, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. G. Jäger, “Gähler's neighbourhood condition for lattice-valued convergence spaces,” Fuzzy Sets and Systems, vol. 204, pp. 27–39, 2012. View at Publisher · View at Google Scholar
  15. L. Li, Many-valued convergence, many-valued topology, and many-valued order structure [Ph.D. thesis], Sichuan University, 2008, (Chinese).
  16. L. Li and Q. Jin, “On adjunctions between Lim, SL-Top, and SL-Lim,” Fuzzy Sets and Systems, vol. 182, no. 1, pp. 66–78, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. L. Li and Q. Jin, “On stratified L-convergence spaces: pretopological axioms and diagonal axioms,” Fuzzy Sets and Systems, vol. 204, pp. 40–52, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. Orpen and G. Jäger, “Lattice-valued convergence spaces: extending the lattice context,” Fuzzy Sets and Systems, vol. 190, pp. 1–20, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. W. Yao, “On many-valued stratified L-fuzzy convergence spaces,” Fuzzy Sets and Systems, vol. 159, no. 19, pp. 2503–2519, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. H. Boustique and G. Richardson, “A note on regularity,” Fuzzy Sets and Systems, vol. 162, no. 1, pp. 64–66, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. H. Boustique and G. Richardson, “Regularity: lattice-valued Cauchy spaces,” Fuzzy Sets and Systems, vol. 190, pp. 94–104, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. P. V. Flores, R. N. Mohapatra, and G. Richardson, “Lattice-valued spaces: fuzzy convergence,” Fuzzy Sets and Systems, vol. 157, no. 20, pp. 2706–2714, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. P. V. Flores and G. Richardson, “Lattice-valued convergence: diagonal axioms,” Fuzzy Sets and Systems, vol. 159, no. 19, pp. 2520–2528, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. B. Losert, H. Boustique, and G. Richardson, “Modifications: lattice-valued structures,” Fuzzy Sets and Systems, vol. 210, pp. 54–62, 2013. View at Google Scholar
  25. L. Li and Q. Jin, “p-Topologicalness and p-regularity for lattice-valued convergence spaces,” Fuzzy Sets and Systems, 2013. View at Publisher · View at Google Scholar
  26. R. Bělohlávek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic, New York, NY, USA, 2002.
  27. U. Höhle and A. Šostak, “Axiomatic foundations of fixed-basis fuzzy topology,” in Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, U. Höhle and S. E. Rodabaugh, Eds., vol. 3 of The Handbooks of Fuzzy Sets Series, pp. 123–273, Kluwer Academic, London, UK, 1999. View at Google Scholar · View at Zentralblatt MATH
  28. G. Jäger, “Lowen fuzzy convergence spaces viewed as L-fuzzy convergence spaces,” The Journal of Fuzzy Mathematics, vol. 10, pp. 227–236, 2002. View at Google Scholar
  29. G. Preuss, Fundations of Topology, Kluwer Academic, London, UK, 2002.
  30. D. Zhang, “An enriched category approach to many valued topology,” Fuzzy Sets and Systems, vol. 158, no. 4, pp. 349–366, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  31. G. Jäger, “Diagonal conditions for lattice-valued uniform convergence spaces,” Fuzzy Sets and Systems, Fuzzy Sets and Systems, vol. 210, pp. 39–53, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH