播挪运算及其性质

在现有的播挪定义基础上,引入了对偶播挪的概念和任意论域子集族的内并、内交两种新运算,提出了十个定理.它们是：平凡播挪空间定理,最小播挪定理,播挪内运算封闭性定理,播挪任意交定理,播挪上确界定理,播挪运算分配性定理,播挪基判定定理,播挪基闭包定理,播挪基约简定理,播挪基内运算封闭性定理.这些定理对于播挪空间的研究具有一定的理论价值.

Operations of bornologies and their properties

On the basis of the definition of bornology a new conception of a dual-bornology and two new operations of families of subsets of an arbitrary universe are introduced and ten theorems are put forward.They are:theorem of trivial bornological space,theorem of minimal bornology,closedness theorem of internal operations of bornologies,theorem of an arbitrary intersection of bornologies,supremum theorem of bornolo-gies,theorem of distributivity of bornological operations,determination theorem of bornological bas...