- Course Policy
- Textbook: Introduction to Topology and Modern Analysis, G.F. Simmons.
- Course Summary: Download pdf.
- Exam 1. Download pdf.
- HW 1. Download pdf. Due: Friday, August/29.
- HW 2. Download pdf. Due: Friday, September/05. Solutions
- HW 3. Download pdf. Due: Friday, September/12.
- HW 4. Download pdf. Due: Friday, September/29.
- HW 5. Download pdf. Due: Friday, October/17.
- HW 6. Download pdf. Due: Monday, November/03.
Sequential and Weierstrass definitions of continuity for real-valued functions.
- Definition of metric spaces.
- Examples of Metric Spaces: R^n, Cauchy-Schwartz inequality, Space of functions on a closed interval, space of 0-1 sequences.
- Open/Closed sets in Metric Spaces.
- The structure of sets in metric spaces: interior, closure, boundary.
- Continuous functions in metric spaces.
- Completeness, The Baire Category Theorem.
- The contraction mapping theorem.
- Applications: The Perron-Frobenius Theorem.
- Axioms of Topological Spaces. Examples.
- Open sets, Closed sets, Limit Points, Boundary, Closure, Interior.
- Base of Topology.
- Product Topology.
- Connected Spaces. Path-Connected Spaces. Cut points.
- Compact spaces. Heine-Borel Theorem.
- Homeomorphisms and homeomorphic spaces.