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Abstract In 1965 [44], Zadeh introduced the fundamental concept of fuzzy sets which formed the backbone of fuzzy mathematics. Since Chang introduced fuzzy sets theory into topology in 1968 [8]. Wong, Lowen, Hutton, Pu and Liu, etc., discussed respectively various aspects of fuzzy topology [12, 24, 30]. In 1991-1993 [38, 39, 42], Ying introduced the concept of the fuzzifying topology with the semantic method of continuous valued logic. In 1999 Khedr et al. [16] introduced the concept of semiopen sets and semicontinuity in fuzzifying topology. |