拓?fù)淇臻g

內(nèi)容概要

　　本書是一部本科生學(xué)習(xí)拓?fù)淇臻g的基礎(chǔ)教程。引導(dǎo)讀者很好的學(xué)習(xí)拓?fù)渲杏嘘P(guān)幾何的東西什么是最重要的。本書的內(nèi)容分為三大部分，線和面、矩陣空間和拓?fù)淇臻g。書中將大量的數(shù)學(xué)詞匯概念囊括其中，不要求讀者對簡單定理或者集合知識(shí)十分了解，從而減少讀者理解上的難度。收斂定理的應(yīng)用在幫助讀者抓住重點(diǎn)的同時(shí)，逐漸接觸并理解拓?fù)涞母拍睿瑫械闹R(shí)點(diǎn)步步逼近，前九節(jié)重在為本科生講述矩陣空間的知識(shí)，同時(shí)也包括了大量的材料，這些將成為研究生學(xué)習(xí)的教程。本書由(美)布斯科斯著。

書籍目錄

Preface
PART Ⅰ THE LINE AND THE PLANE
Chapter 1 What Topology Is About
Topological Equivalence
Continuity and Convergence
A Few Conventions
Extra: Topological Diversions
Exercises
Chapter 2 Axioms for R
Extra: Axiom Systems
Exercises
Chapter 3 Convergent Sequences and Continuity
Subsequences
Uniform Continuity
The Plane
Extra: Bolzano (1781-1848)
Exercises
ChaPter 4 Curves in the Plane
Curves
Homeomorphic Sets
Brouwer's Theorem
Extra: L.E.J. Brouwer (1881-1966)
PART Ⅱ METRI SPACES
Chapter 5 Metrics
Extra: Camille Jordan (1838-1922)
Exercises
Chapter 6 Open and Closed Sets
Subsets of a Metric Space
Collections of Sets
Similar Metrics
Interior and Closure
The Empty Set
Extra: Cantor (1845-1918)
Exercises
Chapter 7 Completeness
Extra: Meager Sets and the Mazur Game
Exercises
Chapter 8 Uniform Convergence
Extra: Spaces of Continuous Functions
Exercises
Chapter 9 Sequential Compactness
Extra: The p-adic Numbers
Exercises
Chapter 10 Convergent Nets
Inadequacy of Sequences
Convergent Nets
-Extra: Knots
Exercises
Chapter 11 Transition to TOpology
Generalized Convergence
Topologies
Extra: The Emergence of the Professional Mathematician
Exercises
PART Ⅲ TOPOLOGICAL SPACES
Chapter 12 Topological Spaces
Extra: Map Coloring
Exercises
Chapter 13 Compactness and the Hausdorff Property
Compact Spaces
Hausdorff Spaces
Extra: Hausdorff and the Measure Problem
Exercises
Chapter 14 Products and Quotients
Product Spaces
Quotient Spaces
Extra: Surfaces
Exercises
Chapter 15 The Hahn-Tietze-Tong-Urysohn Theorems
Urysohn's Lemma
Interpolation and Extension
Extra: Nonstandard Mathematics
Exercises
Chapter 16 Connectedness
Connected Spaces
The Jordan Theorem
Extra: Continuous Deformation of Curves
Exercises
Chapter 17 Tvchonoffs Theorem
Extra: The Axiom of Choice
Exercises
PAler Ⅳ PosTsciuer
Chapter 18 A Smorgasbord for Further Study
Countability Conditions
Separation Conditions
Compactness Conditions
Compactifications
Connectivity Conditions
Extra: Dates from the History of General Topology
Exercises
Chapter 19 Countable Sets
Extra: The Continuum Hypothesis
A Farewell to the Reader
Literature
Index of Symbols
Index of Terms

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