Introduction to Topology, 3/e (Paperback)
Bert Mendelson
- 出版商: Dover Publications
- 出版日期: 1990-07-01
- 售價: $850
- 貴賓價: 9.5 折 $808
- 語言: 英文
- 頁數: 224
- 裝訂: Paperback
- ISBN: 0486663523
- ISBN-13: 9780486663524
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相關主題
商品描述
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.
The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology.
Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.
商品描述(中文翻譯)
這本簡潔的書籍以其卓越的清晰度、富有想像力和教學性的練習,以及精緻的寫作風格而受到高度讚譽,為基礎拓撲學的理想入門提供了一個理想的介紹。最初設計為一學期課程的教材,針對已經學過微積分定義和定理證明的大學本科生。本書的主要目標是提供對具有數學結構的對象集合或集合的基本主題的簡單而全面的調查。
作者在第1章中以非正式的方式討論了集合論,將可數性的內容保留到第5章,在那裡它出現在緊湊性的上下文中。在第二章中,Mendelson教授討論了度量空間,特別關注可以定義在歐幾里得n-空間上的各種距離函數,並導致普通拓撲。
第3章介紹了拓撲空間的概念,將其作為度量空間概念的一般化。第4章和第5章專門討論了兩個最重要的拓撲性質:連通性和緊湊性。在整本書中,Mendelson博士(曾任史密斯學院數學教授)都包含了許多具有挑戰性和激發性的練習,以幫助學生對所呈現的材料建立牢固的理解。