内函数逼近定理及上溢原理的推广及应用  

The extensions of internal function approximation theorem and overflow theorem and theirs applicitaons

作　　者：陈东立[1] 史艳维[1] 马春晖[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《纯粹数学与应用数学》2006年第1期32-36,共5页Pure and Applied Mathematics

基　　金：陕西省教育厅专项科研基金资助项目(03jk066)

摘　　要：在κ-饱和的非标准模型中,首先推广了内函数逼近定理,并用这一推广定理证明了著名的A sco li定理;其次将上(下)溢原理推广到一般的定向集上,并证明了拓扑空间中单子的一些性质,给出了无穷小延伸定理的一个简单证明.In the k-saturated nonstandard model, the internal function approximation theorem was extended at first. By this theorem, the famous Ascoli theorem was proved. Then the overflow and underflow theorems were extended to a directed set. As their applications, some properties of monads on topological space were obtained and a proof of the infinitesimal prolongation theorem on nets was presented.

关 键 词：饱和 逼近定理 上溢原理 单子 无穷小延伸定理 

分 类 号：O141.41[理学—数学]