Spring MAT 147

Topology

MAT 147

Professor: Jennifer Schultens
Office: Kerr 577
Office hours: M 10-10:50, W 12-12:50, F 2:10-3
Phone: 754-9374
www.math.ucdavis.edu/~jcs/147.html
e-mail: jcschultens at ucdavis dot edu

TA: Chris Jerdonek
Office: Kerr 460
Office hours: M 12:10-1, W 2:10-3, F 12:10-1

Book: Munkres's: Topology, An Introduction
Cost: $101

Basic notions of point-set topology: Topological Spaces and Continuous Functions; Connectedness and Compactness; Countability and Separation Axioms; Topics in Metric Spaces. Prerequisite: courses 108, 127A.

Attendance is not mandatory but is expected. There will be homework, 5 quizzes, one midterm and a final exam in this class. The quizzes will be given unannounced but will consist of problems very similar to those on the homework.

Homework will be due on Fridays. It will consist of all problems assigned for the previous friday, monday and wednesday. E.g., on Friday, April 9, homework assigned April 2, April 5 and April 7 will be due! Homework must be handed in to the box labelled "MAT 147 - new homework" in the basement of Wellman.

Homeworks left in my mailbox, slid under my door or handed to me will be discarded.

Your grade will be calculated in the following way: Homework 10%, Quizzes 25%, Midterm 25%, Final Exam 40%.

Excerpts from homeworks:

Quizzes:

Midterm:

Midterm

Day Subject Homework Other Comments

April 2 Topological Spaces p. 83: 1, 2, 4

April 5 Basis for a Topology p. 83: 5, 6, 7

April 7 Basis for a Topology (continued)

April 9 The Order Topology Study the examples in the text. no office hours (I talk at CSU Chico 4pm)

April 12 The Product Topology Study the examples in the text.

April 14 The Subspace Topology p. 91: 1, 2, 3, 4, 6*

April 16 Closed Sets and Limit Points p. 100: 1, 5, 6

April 19 Closed Sets and Limit Points (continued) p. 100: 10, 11, 12, 13*

April 21 Continuous Functions no office hours (I travel to give a lecture series at OK State University)

April 23 Continuous Functions (continued) p. 111: 3, 5, 6, 8* TA substitutes - possibly a quiz - no office hours (I lecture at OK State University)

April 26 Continuous Functions (continued)

April 28 The Metric Topology

April 30 The Metric Topology (continued) p. 126: 1, 2, 3, 9*

May 3 The Metric Topology (continued)

May 5 The Quotient Topology p. 145: 1, 2 (These two problems are optional)

May 7 MIDTERM

May 10 Connected Spaces p. 152: 1, 2, 4*, 7

May 12 Connected Subspaces of the Real Line p. 157: 1(a), 1(c), 2 no office hours (I travel to the AMS-SMM Joint Meeting)

May 14 Curious Examples of Topological Spaces TA substitutes - possibly a quiz - no office hours (I attend the AMS-SMM conference)

May 17 Compact Spaces p. 170: 1, 2, 3*, 4, 8

May 19 Compact Spaces (continued)

May 21 Compact Subspaces of the Real Line p. 177: 4, 5 (This problem is optional - a valuable reading exercise), 6b-e

May 24 The Countability Axioms p. 194: 10 (This problem is optional - because we haven't covered the product topology for a product with infinitely many factors), 11*

May 26 The Separation Axioms

May 28 The Separation Axioms (continued) p. 199: 1, 3

May 31 HOLIDAY: MEMORIAL DAY

June 2 Normal Spaces p. 205: 1, 3 (see page 182 for the definition of locally compact, you may quote Theorem 29.1 and Theorem 32.3), 4*

June 4 The Urysohn Lemma & The Urysohn Metrization Theorem p. 212: 1, 2; p. 218: 1, 2 (this problem is optional), 3*

June 7 An Introduction to Dimension Theory

June 9 Review

June 14 Review by Chris Jerdonek 4-6pm, 212 Wellman

June 16 FINAL EXAM 10:30am - 12:30pm, 119 Wellman

Day	Subject	Homework	Other Comments
April 2	Topological Spaces	p. 83: 1, 2, 4
April 5	Basis for a Topology	p. 83: 5, 6, 7
April 7	Basis for a Topology	(continued)
April 9	The Order Topology	Study the examples in the text.	no office hours (I talk at CSU Chico 4pm)
April 12	The Product Topology	Study the examples in the text.
April 14	The Subspace Topology	p. 91: 1, 2, 3, 4, 6*
April 16	Closed Sets and Limit Points	p. 100: 1, 5, 6
April 19	Closed Sets and Limit Points (continued)	p. 100: 10, 11, 12, 13*
April 21	Continuous Functions		no office hours (I travel to give a lecture series at OK State University)
April 23	Continuous Functions (continued)	p. 111: 3, 5, 6, 8*	TA substitutes - possibly a quiz - no office hours (I lecture at OK State University)
April 26	Continuous Functions (continued)
April 28	The Metric Topology
April 30	The Metric Topology (continued)	p. 126: 1, 2, 3, 9*
May 3	The Metric Topology (continued)
May 5	The Quotient Topology	p. 145: 1, 2 (These two problems are optional)
May 7	MIDTERM
May 10	Connected Spaces	p. 152: 1, 2, 4*, 7
May 12	Connected Subspaces of the Real Line	p. 157: 1(a), 1(c), 2	no office hours (I travel to the AMS-SMM Joint Meeting)
May 14	Curious Examples of Topological Spaces		TA substitutes - possibly a quiz - no office hours (I attend the AMS-SMM conference)
May 17	Compact Spaces	p. 170: 1, 2, 3*, 4, 8
May 19	Compact Spaces (continued)
May 21	Compact Subspaces of the Real Line	p. 177: 4, 5 (This problem is optional - a valuable reading exercise), 6b-e
May 24	The Countability Axioms	p. 194: 10 (This problem is optional - because we haven't covered the product topology for a product with infinitely many factors), 11*
May 26	The Separation Axioms
May 28	The Separation Axioms (continued)	p. 199: 1, 3
May 31	HOLIDAY: MEMORIAL DAY
June 2	Normal Spaces	p. 205: 1, 3 (see page 182 for the definition of locally compact, you may quote Theorem 29.1 and Theorem 32.3), 4*
June 4	The Urysohn Lemma & The Urysohn Metrization Theorem	p. 212: 1, 2; p. 218: 1, 2 (this problem is optional), 3*
June 7	An Introduction to Dimension Theory
June 9	Review
June 14	Review by Chris Jerdonek	4-6pm, 212 Wellman
June 16	FINAL EXAM	10:30am - 12:30pm, 119 Wellman