Accumulation Point and C. T. Yang’s Theorem in L-fuzzy Topological Spaces*

The investigations on accumulation point in fuzzy topological spaces L-fuzzy topological spaces.have lasted for more than 16 years e.g., see w9x, w11x, w6x, w15x, w17x, w20x, w13x, w4x, w1x, w18x, w16x, w5x.. Amongst these researches, the notion introduced in w9x even yielded the fuzzy form of the famous C. T. Yang’s Theorem. But, however, the main basic problem, making the derivation operator derived from it preserve finite joins, is still unsolved; even only inclusion order of subsets cannot be preserved. Compared with the fundamental position of this concept standing at in topology, this shortage is obvious. With a new operation possessing many quite nice properties, the so-called ‘‘quasi-difference’’ between two L-fuzzy subsets, a reasonable definition is introduced for this basic notion in this paper which possesses the wanted properties and, applying its nice property, the L-fuzzy form of the C. T. Yang’s Theorem is proved.