Topology

从点集拓扑的角度看数学分析，从空间映射的角度看线性代数

1. Topological Spaces
1. Topology
2. Open Sets
3. Finite-Closed Topology
2. The Euclidean Topology
1. Euclidean Topology
2. Basis for a Topology
3. Basis for a Given Topology
3. Limit Points
1. Limit Points and Closure
2. Neighbourhoods
3. Connectedness
4. Homeomorphisms
1. Subspaces
2. Homeomorphisms
3. Non-Homeomorphic Spaces
5. Continuous Mappings
1. Continuous Mappings
2. Intermediate Value Theorem
6. Metric Spaces
1. Metric Spaces
2. Convergence of Sequences
3. Completeness
4. Contraction Mappings
5. Baire Spaces
7. Compactness
1. Compact Spaces
2. The Heine-Borel Theorem
8. Finite Products
9. Countable Products
10. Tychonoff’s Theorem
11. Quotient Spaces
12. The Stone-Weierstrass Theorem

线性代数知识体系

主要参考教材：

• Finite-Dimensional Vector Spaces
• Linear Algebra Done Right

画图及公式编辑软件：

• OmniGraffle
• LaTeXiT

课程笔记：「Speak English Professionally」

课程名称：「Speak English Professionally: In Person, Online & On the Phone」

开课学校：「乔治亚理工学院」