On the Convergence Structure of L-Topological Spaces and Graded Continuity in L-Topological Spaces, II.
by
Mustafa Demirci
Akdeniz University, Antalya

Building on the work presented in Part I, the convergence structure of L-topological spaces, formed using L-neighborhood systems, L-filters and the convergence of L-filters in [1], are introduced, and new results in this direction are proved. Furthermore, by introducing the L-fuzzy set theoretic definition of fuzzy inclusion, a generalized version of the fuzzy inclusion in [2-3], and using L-neighborhood systems, the notions of the L-continuity degree of a function at a crisp point and the L-continuity degree of a function are defined as a measure of the local continuity of a function and a measure of the global continuity of a function, respectively. It is then shown that various results concerning continuous functions in classical topological spaces can be established using these degrees in L-topological spaces.

References

1. U. Höhle and A.P. Sostak, Axiomatic Foundations of Fixed-Basis Fuzzy Topology, in Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, eds. U. Höhle and S. E. Rodabaugh (Kluwer Academic, Boston, 1999), 123-272.
2. A. P. Sostak, On a Fuzzy Topological Structure, Suppl. Rend. Circ. Matem. Palermo. Ser. II, 11, 1985, 89-103.
3. A. P. Sostak, Two Decades of Fuzzy Topoloy: Basic Ideas, Notations and Results, Russian Math. Surveys 44, 1989, 125-186.

Date received: July 24, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagx-54.