18.901
Introduction to Topology
Introduces topology, covering topics fundamental to modern analysis and geometry. Topological spaces and continuous functions, connectedness, compactness, separation axioms, covering spaces, and the fundamental group.
Fall 2004
Topics
- Ses 1: Logic and Foundations
- Ses 2-3: Relations, Cardinality, Axiom of Choice
- Ses 4-5: Topologies, Closed Sets
- Ses 6-7: Continuous Functions, Arbitrary Products
- Ses 8-9: Metric Topologies
- Ses 10: Quotient Topology
- Ses 11-12: Connected Spaces, Compact Spaces
- Ses 13-14: More about Compactness
- Ses 15: Well-ordered Sets, Maximum Principle
- Ses 17-18: Countability and Separation Axioms
- Ses 19-20: Urysohn Lemma, Metrization
- Ses 21: Tietze Theorem
- Ses 22-23: Tychonoff Theorem, Stone-Cech Compactification
- Ses 24-25: Baire Spaces, Dimension Theory
- Ses 26: Imbedding in Euclidean Space
Readings
- WEEK #: 1 · TOPICS: Ses 1: Logic and Foundations · READINGS: Sec. 1-2
- WEEK #: 2 · TOPICS: Ses 2-3: Relations, Cardinality, Axiom of Choice · READINGS: Sec. 3-9
- WEEK #: 3 · TOPICS: Ses 4-5: Topologies, Closed Sets · READINGS: Sec. 12-17
- WEEK #: 4 · TOPICS: Ses 6-7: Continuous Functions, Arbitrary Products · READINGS: Sec. 18-19
- WEEK #: 5 · TOPICS: Ses 8-9: Metric Topologies · READINGS: Sec. 20-21
- WEEK #: 6 · TOPICS: Ses 10: Quotient Topology · READINGS: Sec. 22
- WEEK #: 7 · TOPICS: Ses 11-12: Connected Spaces, Compact Spaces · READINGS: Sec. 23-26
- WEEK #: 8 · TOPICS: Ses 13-14: More about Compactness · READINGS: Sec. 27-29
- WEEK #: 10 · TOPICS: Ses 17-18: Countability and Separation Axioms · READINGS: Sec. 30-32
- WEEK #: 11 · TOPICS: Ses 19-20: Urysohn Lemma, Metrization · READINGS: Sec. 33-34
- WEEK #: 12 · TOPICS: Ses 21: Tietze Theorem · READINGS: Sec. 35
- WEEK #: 13 · TOPICS: Ses 22-23: Tychonoff Theorem, Stone-Cech Compactification · READINGS: Sec. 37-38
- WEEK #: 15 · TOPICS: Ses 26: Imbedding in Euclidean Space · READINGS: Sec. 36, pp. 309-313
Prerequisites & course information
Subject meets with 18.9011 Prereq: 18.100A , 18.100B , 18.100P , 18.100Q , or permission of instructor U (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2004
- MIT OCW readings ↗
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.