Course Code: B12003Y
Course Name: Basic Topology
Lecture Time: 20 weeks, 2 sessions/week, 2 hours/session
This course is designed for undergraduate students with major in mathematical sciences and is also one of the required courses for other physics majors. The main contents of this course include: (1)Point set topology；(2) Combinatorial topology (the origin of algebraic topology); (3) Algebraic topology.
Since topology is a branch of geometry, the aim of this class is to improve students’ ability of geometric imagination on geometry and their ability to analyze geometry problems. In particular, the teacher will introduce the main characteristics and methods of topological space together with the basic theory of topology to lay foundation for future courses.
Topics and Schedule
2.1.Open sets and closed sets
2.4.Tietze extension theorem
3.1.Closed sets in Euclidean space
3.2.Heine Borel theorem
4.1.The creation of the Mobius strip
5.5.Brouwer fixed-point theorem
5.7.The boundary of surface
6.1.Simplicial subdivision of spaces
6.4.The Homotopy groups of complexes
6.5.Simplicial division of Orbit space
7.2.Simplex division and Orientation
7.4.Calculation of digging and adding
8.1.Closed line and boundary
9.1.The continuous map of sphere
9.2.Euler Poincaré equation
6.3.Borsuk Ulam theorem
6.4.Lefschetz fixed-point theorem
The grades include midterm examination, final examination, and assignments of weekly homework.
Armstrong, Mark Anthony. Basic topology. Springer Science & Business Media(Chinese Version), translated by Yifeng Zhang.
Chengye You, Basic topology , Beijing University Press, 1997 (Chinese Version)
To be added