L-Fuzzy Derived Set Inequality,Closure Inequality And Good Spaces

In general topology, it is clear that there are three formulas G∩A~d(?)(G∩A)~d,G∩A~-(?)(G∩A)~-, F∪A~0(?)(F∪A)~0 hold, with regard to open sets G,closed sets F and arbitrary L-fuzzy subsets A of L~X. Unfortunately , however they do not hold in L-fuzzy topology. there are one or two authors of some early papers in L-fuzzy topology generalize parallely them to general topology, this is certainly wrong. this paper discusses the conditions of the derived sets inequality G∧A~d≤(G∧A)~d and closure inequality G∧A~-≤(G∧A)~- hold for arbitrary open sets G and arbitrary L-fuzzy subsets A of L~X with regard to this question in the L-fuzzy topological space (L~X,δ), further more, studies L-fuzzy topological space which these inequality hold has properties. The primary studies are the following:1 Derived set inequalityNotion of derived set defines based on the notion of accumulation point, one point corresponds one accumulation point, so far, academe gives a lot of notions of accumulation point, therein, the most representative and familiar accumulation point is two kinds of different accumulation points defined by professor Wang guo–jun and Liu ying–ming, they educe two kinds of derived sets inequality, this paper discusses the conditions under which two kinds of derived sets inequality. the primarily results are :⑴In the L-fuzzy topological space with Boole lattices L, two kinds of derived sets inequality hold. ⑵In induced spaces and weakly induced spaces, lattices L slightly restricts, two kinds of derived set inequality hold, too.⑶Lattices L with no restrictions, in induced spaces or weakly induced spaces, two kinds of derived sets inequality do not hold. this paper gives corresponding counterexample.2 L-fuzzy good spacesPaper five discusses the conditions of the hold about the closure inequality G∧A~d≤(G∧A)~d, this paper defines L-fuzzy topological space satisfing closure inequality to L-fuzzy good spaces. firstly, we indicate L-fuzzy good spaces are differ from stratified spaces, induced spaces and weakly induced spaces, is an interesting L-fuzzy topological spaces, secondly, we prove L-fuzzy good spaces possesses transmissibility and sumable, but production do not hold.3 Fuzzifying derived set inequality and closure inequalityWe generalize derived sets inequality and closure inequality in L-fuzzy topological spaces to fuzzifying topological spaces, find corresponding results.