L-拓扑空间广义模糊半紧性

Generalized fuzzy semicompactness in L-topological spaces

借助广义半开L-集、广义半闭L-集和不等式,在L-拓扑空间定义了广义模糊半紧性,这里L是完备的de Morgan代数.这个定义不依赖于L的结构,并且L不要求分配性.证明了:①广义模糊半紧性L-集和广义半L-闭集的交是广义模糊半紧性;②当L是完备的Heyting代数时,两个广义模糊半紧L-集的并也是广义模糊半紧的;③当L是完备的Heyting代数时,在广义半不定映射下,原像是广义模糊半紧的,则像也是广义模糊半紧的.此外,当L是完全分配的de Morgan代数,给出了它的许多等价刻画.

By means of generalized fuzzy semiopen L-set,generalized fuzzy semiopen L-set and inequality,we introduce generalized fuzzy semicompactness in L-spaces where L is a complete de Morgan algebra.This definition does not rely on the structure of basis lattice L and no distributivity is required.It is proved that①The intersection of a generalized fuzzy semicompact L-set and a generalized semiclosed L-set is a generalized fuzzy semicompact L-set.②When L is complete Heyting algebra,the union of two generalized fuzzy semicompact L-set is semicompact L-set.③When L is complete Heyting algebra,the generalized semiirresolute image of a generalized fuzzy semicompact L-set is a generalized fuzzy semicompact L-set.Moreover,when L is a completely distributive de Morgan algebra,many characterizations of it are given.