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ON THE CONVERGENCE STRUCTURE OF L-TOPOLOGICAL SPACES AND THE CONTINUITY IN L-TOPOLOGICAL SPACES

MUSTAFA DEMİRCİ

Department of Mathematics, Akdeniz University, Antalya, 07058, Turkey

https://doi.org/10.1142/S1793005707000598Cited by:6 (Source: Crossref)

Abstract

A general and a comprehensive theory of fuzzy topological spaces on the basis of a fixed quadruple M = (L, ≤, ⊗, *), where (L, ≤), ⊗ and *, respectively, denote a complete lattice and binary operations on L satisfying some further axioms, was introduced by Höhle and Šostak. L-topological spaces, convergence structure of L-topological spaces and L-continuous functions form an important part of their work. The present paper continues the study in this area, and provides new results on the convergence structure of L-topological spaces and the continuity in L-topological spaces.

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References

U. Höhle and A. P. Šostak, Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, eds. U. Höhle and S. E. Rodabaugh (Kluwer Academic, Boston, 1999) pp. 123–272. Crossref, Google Scholar
C. L. Chang, J. Math. Anal. Appl. 24, 182 (1968). Crossref, Web of Science, Google Scholar
J. A. Goguen, J. Math. Anal. Appl. 43, 734 (1973). Crossref, Web of Science, Google Scholar
U. Höhle and A. Šostak, Fuzzy Sets and Systems 73, 131 (1995). Crossref, Web of Science, Google Scholar
U. Höhle, Manuscripta Math. 26, 299 (1978). Google Scholar
U. Höhle, Fuzzy Sets and Systems 13, 39 (1984). Crossref, Web of Science, Google Scholar
B. Hutton, J. Math. Anal. Appl. 50, 74 (1975). Crossref, Web of Science, Google Scholar
B. Hutton, Topology Appl. 11, 59 (1980). Crossref, Web of Science, Google Scholar
R. Lowen, J. Math. Anal. Appl. 56, 621 (1976). Crossref, Web of Science, Google Scholar
R. Lowen, J. Math. Anal. Appl. 64, 446 (1978). Crossref, Web of Science, Google Scholar
A. P. Šostak, Suppl. Rend. Circ. Matem. Palermo. Ser. II 11, 89 (1985). Google Scholar
A. P. Šostak, Russian Math. Surveys 44, 125 (1989). Crossref, Google Scholar
L. N. Stout, Manuscripta Math. 17, 1 (1975). Crossref, Web of Science, Google Scholar
G. Birkhoff , Lattice Theory , 3rd edn. , Amer. Math. Soc. Colloquium Publications ( Amer. Math. Soc. , RI , 1967 ) . Google Scholar
U. Höhle, Non-Classical Logics and Their Applications to Fuzzy Subsets 32, eds. U. Höhle and E. P. Klement (Kluwer, Dordrecht, 1995) pp. 53–106. Crossref, Google Scholar
U. Höhle, Non-Classical Logics and Their Applications to Fuzzy Subsets 32, eds. U. Höhle and E. P. Klement (Kluwer, Dordrecht, 1995) pp. 127–157. Crossref, Google Scholar