• Home


• 461-001 Home


• Syllabus


• Schedule and HW

Metric and Topological Spaces
MTH 461-001

Schedule and Topics Covered

Date	Topic/Section	Assignments and Reading
8/28	Welcome, and Functions	Read Syllabus
8/30	Functions and Relations	Read book pages 3 -- 29
9/1	Order Relations	Homework 1 Due 9/8 the .tex file
9/4	Holiday - no class
9/6	Countability	Read book pages 30 -- 50
9/8	Cardinality and Sizes of Infinity Homework 1 Due in Class Today!	Homework 2 Due 9/15 the .tex file
9/11	The Axiom of Choice	Read book pages 52 -- 71
9/13	Well-Ordered Sets
9/15	Maximum Principal Homework 2 Due in Class Today!	Homework 3 Due 9/23 the .tex file
9/18	Topological Spaces	Read book pages 75 -- 86
9/20	Basis for a Topology
9/22	More on Bases Homework 3 Due Before Midnight 9/23	Homework 4 Due 10/1 the .tex file
9/25	The Order Topology	Read book pages 86 -- 91
9/27	The Product Topology
9/29	The Subspace Topology Homework 4 Due Before Midnight 10/1	Homework 5 Due 10/8 the .tex file
10/2	Closed Sets and Interiors	Read book pages 92 -- 100
10/4	Set Closure and Limit Points
10/6	Hausdorff Spaces Homework 5 Due Before Midnight 10/8	Homework 6 Due 10/15 the .tex file
10/9	Continuous Functions	Read book pages 102 -- 111
10/11	Homeomorphisms
10/13	Constructing Continuous Functions Homework 6 Due Before Midnight 10/15	Homework 7 Due 10/29 the .tex file
10/16	The Product Topology	Read book pages 112 -- 117
10/18	Product Topology Continued
10/20	MIDTERM EXAM
10/23	Fall Break - no class
10/25	ASYNCHRONOUS LECTURE	Read pages 119 -- 126
10/27	Metric Spaces Homework 7 Due Before Midnight 10/29	Homework 8 Due 11/5 the .tex file
10/30	Metrizable Spaces
11/1	On Standard Metrics for Rn
11/3	ASYNCHRONOUS LECTURE Homework 8 Due Before Midnight 11/5	Homework 9 Due 11/12 the .tex file
11/6	Continuity and Metrizability	Read pages 129 -- 133
11/8	Uniform vs Pointwise Convergence
11/10	The Quotient Topology Homework 9 Due Before Midnight 11/12	Homework 10 Due 11/19 the .tex file
11/13	Quotient Maps	Read pages 136 -- 144
11/15	Quotient Spaces
11/17	Properties of Quotient Maps Homework 10 Due Before Midnight 11/19	Homework 11 Due 12/3 the .tex file
11/20	Inducing Homeomorphisms
11/22	ASYNCHRONOUS LECTURE
11/24	Thanksgiving Break - no class
11/27	Connected Spaces	Read pages 147 -- 152
11/29	Connected Subspaces of R	Read pages 153 -- 157
12/1	ASYNCHRONOUS LECTURE Homework 11 Due Before Midnight 12/3	Homework 12 Due 12/10 the .tex file
12/4	Compact Spaces	Read pages 163 -- 170
12/6	Properties of Compact Spaces
12/8	Review Homework 12 Due Before Midnight 12/10
12/13	Final Exam Time	7:45am - 9:45am