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http://dx.doi.org/10.5391/IJFIS.2009.9.2.115

L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic  

Zeyada, Fathei M. (Department of Mathematics, Faculty of Science, Al-Azhar University)
Abd-Allahand, M. Azab (Department of Mathematics, Faculty of Science, Al-Azhar University)
Mousa, A.K. (Department of Mathematics, Faculty of Science, Al-Azhar University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.9, no.2, 2009 , pp. 115-127 More about this Journal
Abstract
In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.
Keywords
(2, L)-topology; Complete residuated lattice; Pre-open set; Pre-separation axioms;
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