Oᵣ-convergence and weak Oᵣ-convergence of nets and their applications

• Li, Hong-Yan ^[1] ; Shi, Fu-Gui ^[2]
  1. [1] Shandong Institute of Business and Technology

     Shandong Institute of Business and Technology

     China

     
  2. [2] Beijing Institute of Technology

     Beijing Institute of Technology

     China

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 27, Nº. 1, 2008, págs. 81-96
• Idioma: inglés
• DOI: 10.4067/S0716-09172008000100005
• Enlaces
  • Texto completo
• Resumen

  • In this paper, the theory of Oᵣ-convergence and weak Oᵣ-convergence of nets is introduced in L-topological spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence.It can be used to characterize preclosed sets, preopen sets, δ-closed sets, δ-open sets, near compactness and near S∗-compactness.

• Referencias bibliográficas
  • Citas [1] Azad K.K., On Fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. and Appl., 82, pp. 14—32,...
  • [2] Bai S.Z., Q-convergence of fuzzy nets and weak separation axioms in fuzzy lattices, Fuzzy Sets and Systems 88, pp. 379-386, (1997)
  • [3] Bai S.Z., Pre-semiclosed Sets and PS-convergence In L-fuzzy Topological Space, J. Fuzzy Math. 2, pp. 497-509, (2001).
  • [4] Bai S.Z., PS-convergence theory of fuzzy nets and its applications, Information Sciences 153, pp. 237-346, (2003).
  • [5] Bhaumik R.N. and Mukherjee A., Fuzzy completely continuous mappings, Fuzzy Sets and Systems 56, pp. 243—246, (1993).
  • [6] Chang C.L., Fuzzy topological spaces, J. Math. Anal. Appl. 24, pp. 182-190, (1968).
  • [7] Chen S.L. and Cheng J.S., θ-convergence of nets of L-fuzzy sets and its applications, Fuzzy Sets and Systems 86, pp. 235-240, (1997).
  • [8] Chen S.L. and Wu J.R., SR-convergence theory in fuzzy lattices, Information Sciences 125, pp. 233-247, (2000).
  • [9] Chen S.L., Chen S.T. and Wang X.G., σ-convergence theory and its applications in fuzzy lattices, Information Sciences 165, pp. 45—58,...
  • [10] Dwinger P., Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Nederl. Akad. Wetensch....
  • [11] Ganguly S. and Saha S., A note on δ-continuity and δ-connected sets in fuzzy set theory, Sima. Stevin 62, pp. 127—141, (1988).
  • [12] Georgiou D.N. and Papadopoulos B.K., On fuzzy θ-convergences, Fuzzy Sets and Systems 116, pp. 385—399, (2000).
  • [13] Gierz G. and et al., A compendium of continuous lattices, Springer Verlag, Berlin, (1980).
  • [14] Katsaras A.K., Convergence in fuzzy topological spaces, Fuzzy Math. 3, pp. 35-44, (1984).
  • [15] Liu Y.M. and Luo M.K., Fuzzy topology, World Scientific Singapore, (1997).
  • [16] Mashhour A.S.,Ghanim M.H. and Alla M.A.F., On fuzzy noncontinuous mappings, Bull. Calcutta Math. Soc. 78, pp. 57—69, (1986).
  • [17] Mukherjee M.N. and Ghosh B., Some stronger forms of fuzzy continuous mappings on fuzzy topological spaces, Fuzzy Sets and Systems 38,...
  • [18] Pu B.M. and Liu Y.M., Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76,...
  • [19] Shi F.G. and Zheng C.Y., O-convergence of fuzzy nets and its applications, Fuzzy Sets and Systems 140, pp. 499-507, (2003).
  • [20] Shi F.G., A new notion of fuzzy compactness in L-topological spaces, Information Sciences 173, pp. 35—48, (2005)
  • [21] Shi F.G. and Xu Z.G., Near compactness in L-topological spaces, Submitted.
  • [22] Wang G.J., Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xi’an, (1988) (in Chinese).
  • [23] Wang G.J., A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl. 94, pp. 1—23, (1983).