| 内函数逼近定理及上溢原理的推广及应用 |
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| 引用本文： | 陈东立,史艳维,马春晖.内函数逼近定理及上溢原理的推广及应用[J].纯粹数学与应用数学,2006,22(1):32-36. |
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| 作者姓名： | 陈东立 史艳维 马春晖 |
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| 作者单位： | 西安建筑科技大学理学院,陕西,西安,710055;西安建筑科技大学理学院,陕西,西安,710055;西安建筑科技大学理学院,陕西,西安,710055 |
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| 基金项目： | 陕西省教育厅专项科研基金资助项目(03jk066) |
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| 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.
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| 关 键 词： | 饱和 逼近定理 上溢原理 单子 无穷小延伸定理 |
| 文章编号： | 1008-5513（2006）01-0032-05 |
| 收稿时间： | 2004-11-13 |
| 修稿时间： | 2004年11月13日 |
The extensions of internal function approximation theorem and overflow theorem and theirs applicitaons |
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| CHEN Dong-li,SHI Yan-wei,MA Chun-hui.The extensions of internal function approximation theorem and overflow theorem and theirs applicitaons[J].Pure and Applied Mathematics,2006,22(1):32-36. |
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| Authors: | CHEN Dong-li SHI Yan-wei MA Chun-hui |
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| Abstract: | 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. |
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| Keywords: | k-saturation approximation theorem the overflow theorem monad the infinitesimal prolongation theorem |
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