L-拓扑空间广义模糊半紧性  

Generalized fuzzy semicompactness in L-topological spaces

作　　者：徐振国[1] 刘梦国 XU Zhenguo;LIU Mengguo(National Science and Technology Infrastructure Center Beijing, Beijing 100038, China;Shenyang Tongze High School, Shenyang 110011, China)

机构地区：[1]国家科技基础条件平台中心,北京100038 [2]沈阳市同泽高中,辽宁沈阳110011

出　　处：《辽宁师范大学学报（自然科学版）》2021年第4期450-453,共4页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：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.

关 键 词：L-拓扑空间 广义半开L-集 广义半闭L-集 广义模糊半紧性 

分 类 号：O189.1[理学—数学]