SciELO - Scientific Electronic Library Online

 
vol.27 issue1DEUX EXEMPLES DE CALCUL EXPLICITE DE COHOMOLOGIE DE DOLBEAULT FEUILLETÉESHARP INEQUALITIES FOR FACTORIAL n author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.27 no.1 Antofagasta May 2008

http://dx.doi.org/10.4067/S0716-09172008000100005 

Proyecciones Journal of Mathematics
Vol. 27, Nº 1, pp. 81-96, May 2008.
Universidad Católica del Norte
Antofagasta - Chile


OR-CONVERGENCE AND WEAK OR-CONVERGENCE OF NETS AND THEIR APPLICATIONS


HONG—YAN LI 1
FU—GUI SHI 2

1 Shandong Institute of Business and Technolgy, China
2 Beijing Institute of Technology, China

Correspondencia a:



Abstract
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.


Key words : L-space; neighborhood; strong neighborhood; OR-convergence; weak OR-convergence
Mathematics Subject Classification (2000): 54A40.

REFERENCES
[1] Azad K.K., On Fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. and Appl., 82, pp. 14—32, (1981)
[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., s-convergence theory and its applications in fuzzy lattices, Information Sciences 165, pp. 45—58, (2004).
[10] Dwinger P., Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Nederl. Akad. Wetensch. indag. Math. 44, pp. 403—414, (1982).
[11] Ganguly S. and Saha S., A note on d-continuity and d-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, pp. 375—387, (1990).
[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, pp. 571-599, (1980).
[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, Subm itted.
[22] Wang G.J., Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xi’an, (1988) (in Ch inese).
[23] Wang G.J., A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl. 94, pp. 1—23, (1983).

HONG—YAN LI
School of Mathematics and Information Science,
Shandong Institute of Business and Technolgy,
Beijing 100081,
China
e-mail : mailto:lihongyan@sdibt.edu.cn

FU—GUI SHI
Department of Mathematics,
Beijing Institute of Technology,
Yantai 264005,
China
e-mail : mailto:fuguishi@bit.edu.cn

Received : November 2006. Accepted : March 2007


Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License