Topology

Math 631-001

The following table contains the schedule for the course. This page will be updated regularly throughout the semester.

Week	Dates		Sections in the Book
1	01/23 - 01/27	I. Topological Spaces
		1. What is Topology?
		2. Topological Spaces	12
2	01/30 - 02/03	3. Basis for a Topology	13
		4. Topology via Order and Products	14, 15
3	02/06 - 02/10	5. The Subspace Topology	16
		6. Closed Sets and Limit Points	17
		7. Limits of Sequences and Separation Axioms	17
4	02/13 - 02/17	8. The Metric Topology	20
		II. Continuity of Functions
		1. Continuous Functions	18
5	02/20 - 02/24	2. Topology of Infinite Products	19
		3. Continuity in Metric Spaces	20, 21
6	02/27 - 03/03	4. The Quotient Topology	22
		III. Connectedness and Compactness
		1. Connected Spaces	23
7	03/06 - 03/10	2. Connected Subspaces of the Real Line	24
	03/09	Midterm Exam (5:55pm-7:10pm)
8	03/13 - 03/17	No class! (Spring Break)
9	03/20 - 03/24	3. Components and Local Connectedness	25
		4. Compact Spaces	26, 27
10	03/27 - 03/31	5. Products of Compact Spaces	26, 37
11	04/03 - 04/07	6. Compactness in the Reals and Metric Spaces	27, 28
		7. Local Compactness	29
12	04/10 - 04/14	IV. Countability and Separation Axioms
		1. The Countability Axioms	30
		2. More Separation Axioms	31, 32
		3. The Urysohn Lemma	33
		4. The Urysohn Metrization Theorem	34
		5. The Tietze Extension Theorem	35
13	04/17 - 04/21	V. Fundamental Group and Covering Spaces
		1. Homotopy of Paths	51
		2. Some Terminology from Group Theory	52
14	04/24 - 04/28	3. The Fundamental Group	52, 59, 60
		4. Covering Spaces and Liftings	53, 54
15	05/01 - 05/05	5. A Sampling of Fundamental Groups	54, 59, 60
		6. Higher Homotopy Groups and Then?
16	05/11	Final Exam (4:30pm-7:15pm)

For the course, I will draw material from the following books:

James R. Munkres, Topology, Second Edition, Pearson Modern Classics, 2017.
Glen E. Bredon, Topology and Geometry, Springer, 2010.
Allen Hatcher, Algebraic Topology, Cambridge, 2001. Can be downloaded as pdf from the author's web page.