18.901 | Fall 2004 | Undergraduate

Introduction to Topology

Readings

The readings are in the textbook: Munkres, James. Topology. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 28 December 1999. ISBN: 0131816292. Please refer to the errata sheet (PDF).

WEEK # TOPICS READINGS
1 Ses 1: Logic and Foundations Sec. 1-2
2 Ses 2-3: Relations, Cardinality, Axiom of Choice Sec. 3-9
3 Ses 4-5: Topologies, Closed Sets Sec. 12-17
4 Ses 6-7: Continuous Functions, Arbitrary Products Sec. 18-19
5 Ses 8-9: Metric Topologies Sec. 20-21
6 Ses 10: Quotient Topology Sec. 22
7 Ses 11-12: Connected Spaces, Compact Spaces Sec. 23-26
8 Ses 13-14: More about Compactness Sec. 27-29
9 Ses 15: Well-ordered Sets, Maximum Principle

Ses 16: Midterm Exam

Sec. 10-11
10 Ses 17-18: Countability and Separation Axioms Sec. 30-32
11 Ses 19-20: Urysohn Lemma, Metrization Sec. 33-34
12 Ses 21: Tietze Theorem Sec. 35
13 Ses 22-23: Tychonoff Theorem, Stone-Cech Compactification Sec. 37-38
14 Ses 24-25: Baire Spaces, Dimension Theory

pp. 264-267, pp. 294-296, pp. 304-308, Theorem 50.6

15 Ses 26: Imbedding in Euclidean Space Sec. 36, pp. 309-313
  Final Exam  

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