朴素集合论 [Naive Set Theory] epub pdf mobi txt 电子书 下载 2024

朴素集合论 [Naive Set Theory] epub pdf mobi txt 电子书 下载 2024

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朴素集合论 [Naive Set Theory] epub pdf mobi txt 电子书 下载 2024

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内容简介

　　Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic settheoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here。

目录

SECTION
PREFACE
1 THE AXIOM OF EXTENSION
2 THE AXIOM OF SPECIFICATION
3 UNORDERED PAIRS
4 UNIONS AND INTERSECTIONS
5 COMPLEMENTS AND POWERS
6 ORDERED PAIRS
7 RELATIONS
8 FUNCTIONS
9 FAMILIES
10 INVERSES AND COMPOSITES
11 NUMBERS
12 THE PEANO AXIOMS
13 ARITHMETIC
14 ORDER
15 THE AXIOM OF CHOICE
16 ZORNS LEMMA
17 WELL ORDERING
18 TRANSFINITE RECURSION
19 ORDINAL NUMBERS
20 SETS OF ORDINAL NUMBERS
21 ORDINAL ARITHMETIC
22 THE SCHRODER-BERNSTEIN THEOREM
23 COUNTABLE SETS
24 CARDINAL ARITHMETIC
25 CARDINAL NUMBERS
INDEX

前言/序言

朴素集合论 [Naive Set Theory] epub pdf mobi txt 电子书 下载 2024

朴素集合论 [Naive Set Theory] 下载 epub mobi pdf txt 电子书 2024

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　　 目次：全书其有四部分，新增加了5章，总共17章。（一）集合论、实数和微积分：集合论；实数体系和微积分。（二）测度、积分和微分：实线上的勒贝格理论；实线上的勒贝格积分；测度和乘积测度的扩展；概率论基础；微分和绝对连续；单测度和复测度。（三）拓扑、度量和正规空间：拓扑、度量和正规空间基本理论；可分离性和紧性；完全空间和紧空间；希尔伯特空间和经典巴拿赫空间；正规空间和局部凸空间。（四）调和分析、动力系统和hausdorff侧都：调和分析基础；可测动力系统；hausdorff测度和分形。

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　　 读者对象：数学及相关专业的大学高年级学生和研究生。

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经典教材，经典图书，建议购买

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很好很满意很好很满意

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正在看着，正在看着。

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this book is suitable for all people in the first process to learn some basis knowlege. i am studying and thinking this course this year. i hope it can play imoportant role for my research level.

评分☆☆☆☆☆

　　 目次：全书其有四部分，新增加了5章，总共17章。（一）集合论、实数和微积分：集合论；实数体系和微积分。（二）测度、积分和微分：实线上的勒贝格理论；实线上的勒贝格积分；测度和乘积测度的扩展；概率论基础；微分和绝对连续；单测度和复测度。（三）拓扑、度量和正规空间：拓扑、度量和正规空间基本理论；可分离性和紧性；完全空间和紧空间；希尔伯特空间和经典巴拿赫空间；正规空间和局部凸空间。（四）调和分析、动力系统和hausdorff侧都：调和分析基础；可测动力系统；hausdorff测度和分形。

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很薄的一本，很简练！很好！

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