Convergence in Smooth Topological Spaces
by
Mutlu Güloglu
Akdeniz University, Antalya
Coauthors: Dogan Çoker

The purpose of this work is to combine the smooth Q-neighborhood system of fuzzy points given by Demirci [4] with the convergence structures of B. Y. Lee et al [7], stated for fuzzy filters using the smooth (pre)filter approach of Ramadan [9].

Since the introduction of fuzzy topology by Chang [22] in the fuzzy set theory of Zadeh [13], fuzzy topology has became a topic of interest in mathematics. In Chang's fuzzy topology, fuzzy open sets were indeed crisp in one sense. On the other hand, openness was fuzzified under the same name of ``fuzzy topology'' by Sostak [10, 11]; ``gradation of openness'' by Chattopadhyay et al [3] and ``smooth topology'' by Ramadan [8]. Later, Demirci [4] defined smooth Q-neighborhood systems of fuzzy points in smooth topological spaces [cf. 12]. Another approach to convergence, the so called fuzzy convergence structure, was initiated by B. Y. Lee et al [7] using the approach of prefilters. In this work we want to introduce ``smooth convergence structures'' in these spaces by means of smooth prefilters defined by Gähler [5, 6], Burton et al [1] and Ramadan [9]; and give the relationships between these structures and the Q-neighborhood systems.

References

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Date received: July 26, 2001