Topology: A Geometric Approach (Oxford Graduate Texts in Mathematics)
暫譯: 拓撲學：幾何方法（Oxford Graduate Texts in Mathematics）

Description

This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses.

The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.

 

 

Table of Contents

Part I: A Geometric Introduction to Topology

1. Basic point set topology

2. The classification of surfaces

3. The fundamental group and its applications

Part II: Covering Spaces, CW Complexes and Homology

4. Covering spaces

5. CW complexes

6. Homology

Selected solutions

References

Index