强L-凸结构的新刻画

New Characterizations of Strong L-convex Structures

为了刻画强L-凸结构,本文借助L-子集之间的模糊包含关系和由其决定的模糊下确界,分别引入了L-格序凸结构、L-格序凸包算子和L-封闭关系,并建立它们与强L-凸结构之间的关系。结果表明,强L-凸空间范畴、L-格序凸空间范畴、L-格序凸包空间范畴和L-封闭空间范畴是同构的。

In order to characterize strong L-convex structures,the concepts of L-ordered convex structures,L-ordered hull operators and L-enclosed relations were introduced by means of fuzzy inclusions orders between L-subsets and their determined fuzzy infimums respectively,and their relations with strong L-convex structures were established.It is finally shown that the categories of strong L-convex spaces,L-ordered convex spaces,L-ordered hull spaces and L-enclosed spaces are isomorphic.