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

In 1999, a comprehensive and powerful approach to fuzzy topological spaces, based on a fixed residuated lattice [1], was introduced by Höhle and Sostak [4]. Their approach unifies various earlier works [2, 3, 5, 8-11, 13-17] in fuzzy topology. L-topological spaces, the convergence structure of L-topological spaces and L-continuous functions form an important part of their work. The present paper continues work in this area, and will be presented in two parts.

The first part covers the necessary background material concerning residuated lattices [4, 6-7, 12] and L-topological spaces [4]. The second part will mostly concentrate on the convergence structure of L-topological spaces and graded continuity in L-topological spaces.

After introducing rudimentary tools concerning residuated lattices and the lattice theoretic background of L-topological spaces, the basic notations concerning L-topological spaces and some new concepts, namely L-closure operators and L-co-topological spaces, which are the complementary notations of the L-interior operators and the L-topological spaces in [4], are given, and connections among L-closure operators, the L-co-topological spaces, the L-interior operators and the L-topological spaces are established.

References

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Date received: July 24, 2001