完备集的性质及应用+文献综述

ABSTRACT In mathematics and related fields, one set is complete set, is a collection of Cauchy sequences converge.In East China Normal University "mathematical analysis" is said the circle principle established set. In "real variable function, that is all points are focal points, all accumulation points belong to the collection collection.
This paper mainly introduces the concept of complete sets of real variable function, structure, properties and complete set of cantor set and the structure, properties and application of shu lang complete set.
Key word：Complete set、Closed set 、Cantor set、complete and nowhere dense set

1  完备集的基本概念    5
1.1  完备集的概念    5
1.2  有关完备集的定义    6
2  完备集的构造与性质    8
2.1  直线上完备集的构造    8
2.2  完备集的性质    8
3  一些特别完备集的性质与应用    9
3.1  康托尔集的构造    10
3.2  康托尔集的性质及证明    10
3．3  康托尔集的应用                 .13
4  疏朗完备集的的性质与应用     . 16

4.1  疏朗完备集的构造. 16
4.2  疏朗完备集的的性质与应用. 16
5  总结    20

1  完备集的基本概念
1．1  完备集的概念

的充要条件为
对任意的 都成立，

1．2  有关完备集的定义

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