文档介绍：An Introduction to Mathematical Analysis
in Economics1
Dean Corbae and Juraj Zeman
December 2002
1Still Preliminary. Not to be photocopied or distributed without permission of
the authors.
2
Contents
1Introduction 13
........................... 13
....................... 17
.................... 19
2SetTheory 21
.......................... 23
Algebraicpropertiesofsetoperations.......... 24
........................ 24
.............................. 25
Equivalencerelations................... 25
Orderrelations...................... 27
................. 30
Restrictionsandextensions............... 32
................. 32
Injectionsandinverses.................. 33
Surjectionsandbijections................ 33
Finite and InÞniteSets...................... 34
.......................... 38
.................... 43
..................... 44
3 The Space of Real Numbers 45
TheFieldAxioms........................ 46
........................ 48
.................... 50
...................... 53
............................. 60
3
4 CONTENTS
.................... 63
..................... 64
4MetricSpaces 65
Convergence ............................ 68
Convergenceoffunctions................. 75
........................... 77
............... 80
........................... 82
Connectedness ........................... 87
...................... 88
Convexsets........................ 92
A Þnite dimensional vector space: Rn .......... 93