环的挖补定理的推广

Generalization of the Ring's Theorem of Taking Out and Patching

将环的挖补定理推广到欧几里得空间,并以推论的形式给出了线性空间的挖补定理;将环的挖补定理推广到非代数系统——拓扑空间,得到了拓扑空间的挖补定理.

As the theorem of taking out and patching in ring is generalied to the Euclidean space,the theorem in linear space is deduced.Furthermore,the theorey is generalized to a nonalgebraic system that is topological space,and then the theorem of taking out and patching in topological space is obtained.