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Generalized Topological Molecular Lattices
Department of Mathematics, Faculty of Science at Qena, South Valley University, Qena, Egypt
Department of Mathematics, College of Science, King Faisal University, Al-Hasa, Saudi Arabia
- 1 Department of Mathematics, Faculty of Science at Qena, South Valley University, Qena, Egypt
- 2 Department of Mathematics, College of Science, King Faisal University, Al-Hasa, Saudi Arabia
Advances in Pure Mathematics·Volume 05 (2015)·Pages 552–559·Published 6 July 2015·DOI10.4236/apm.2015.59051
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Abstract
The aim of this paper is to introduce the concept of generalized topological molecular lattices briefly GTMLs as a generalization of Wang’s topological molecular lattices TMLs, Császár’s setpoint generalized topological spaces and lattice valued generalized topological spaces. Some notions such as continuous GOHs, convergence theory and separation axioms are introduced. Moreover, the relations among them are investigated.
KeywordsGeneralized Topological Molecular LatticesGeneralized Order HomomorphismsConvergence of Molecular NetsSeparation Axioms
- Wang, G.J. (1992) Theory of Topological Molecular Lattices. Fuzzy Sets and Systems, 47, 351-376. http://dx.doi.org/10.1016/0165-0114(92)90301-J
- Chen, Y. (1996) Convergence in Topological Molecular Lattices. Fuzzy Sets and Systems, 84, 97-102. http://dx.doi.org/10.1016/0165-0114(95)00224-3
- Bai, S.Z. (1997) Q-Convergence of Ideals in Fuzzy Lattices and Its Applications. Fuzzy Sets and Systems, 92, 357-363. http://dx.doi.org/10.1016/S0165-0114(96)00174-1
- Chen, S.L. and Wu, Z.X. (2001) Urysohn Separation Property in Topological Molecular Lattices. Fuzzy Sets and Systems, 123, 177-184. http://dx.doi.org/10.1016/S0165-0114(00)00115-9
- El-Saady, K. and Al-Nabbat, F. On Lattice-Valued Generalized Topological Spaces. Submittted for Publication.
- Csàszàr, à. (2002) Generalized Topology, Generalized Continuity. Acta Mathematica Hungarica, 96, 351-357. http://dx.doi.org/10.1023/A:1019713018007
- Al-Nabbat, F. (2015) Lattice-Valued Generalized Neighborhood Structures. To Appear in Southeast Asian Bulletin of Mathematics.
- Yang, Z.Q. (1986) Ideals in Topological Molecular Lattices. Acta Mathematica Sinica, 29, 276-279.
- Chang, C.L. (1968) Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications, 24, 182-190. http://dx.doi.org/10.1016/0022-247X(68)90057-7
- Liu, Y.M. and Luo, M.K. (1997) Fuzzy Topology. World Scientific, Singapore.