拓撲空間(圖書)

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《拓撲空間》是2012年世界圖書出版公司出版的圖書,作者是Gerard Buskes、Arnoud van Rooij。該書一部本科生學習拓撲空間的基礎教程。

基本介紹

  • 中文名:拓撲空間 
  • 作者:Gerard Buskes、Arnoud van Rooij
  • 原作品: Topological Spaces: From Distance to
  • 出版社:世界圖書出版公司
  • 出版時間:2012年1月
  • 頁數:313 頁
  • 定價:39.00 元
  • ISBN:9787510040634
內容簡介,圖書目錄,

內容簡介

《拓撲空間(英文影印版)》是一部本科生學習拓撲空間的基礎教程。引導讀者很好的學習拓撲中有關幾何的東西什麼是最重要的。本書的內容分為三大部分,線和面、矩陣空間和拓撲空間,這些都將是為更進一步學習打下良好的基礎,在講解所熟悉領域的同時,自然而然地透露書不少新的知識點。書中將大量的數學辭彙概念囊括其中,不要求讀者對簡單定理或者集合知識十分了解,從而減少讀者理解上的難度。收斂定理的套用在幫助讀者抓住重點的同時,逐漸接觸並理解拓撲的概念,書中的知識點步步逼近,前九節重在為本科生講述矩陣空間的知識,同時也包括了大量的材料,這些將成為研究生學習的教程。最後,書中講述了拓撲和諸多其他專題,如分析和集合之間的聯繫,通過總結部分,每章都增加了一些除了拓撲知識外的附加知識,這些豐富了內容,使得本書完備性更強。

圖書目錄

preface
parr 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 mt. teac 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 tychonoffs theorem
extra: the axiom of choice
exercises
parr iv postscript
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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