Math 436, Spring 2009

Introduction to Topology

Schedule of lectures

The schedule is only tentative. Please solve all homework problems.

Date
Topic
Homework
Due date
WEEK 1



01/20
Introduction


01/22
1.1 Open sets and definition of a topology
2,5,6,7,8
never
1.2 Basis of a topology
WEEK 2



01/27
1.2 Basis of a topology 11,12,13,15,19
Thu, Feb 5
01/29 1.3 Closed sets 27,28,32,34,37 Thu, Feb 5
WEEK 3


02/03
2.1 Interior and closure of sets


2.2 Limit points
02/05
2.3 The boundary of a set


3.1 The subspace topology
WEEK 4


02/10
3.2 The product topology


02/12
3.3 The quotient topology


3.4 More examples of quotient spaces
WEEK 5


02/17
Review


02/19
EXAM 1


WEEK 6


02/24
4.1 Continuity

02/26
4.2 Homeomorphisms

WEEK 7



03/03 5.1 Metrics

5.3 Properties of metric spaces

03/05
5.4 Metrizability
WEEK 8



03/10
6.1 A first approach to connectedness

03/12
6.2 Distinguishing topological spaces via connectedness

WEEK 9



03/24
6.3 Intermediate Value Theorem

03/26
6.4 Path connectedness
WEEK 10



03/31
Review


04/02
EXAM 2


WEEK 11



04/07
7.1 Compactness


7.2 Compactness in metric spaces
04/09 7.3 The Extreme Value Theorem
7.4 Limit point compactness
WEEK 12



04/14
8.1 Iterating functions
04/16
8.2 Stability

8.3 Chaos
WEEK 13


04/21
9.1 Homotopy

04/23
9.2 Circle functions, degree, and retractions

10.1 The Brouwer Fixed Point Theorem
WEEK 14



04/28
14.1 Manifolds


14.2 Euler characteristcs and compact surfaces
04/30
14.3 Three-manifolds


14.4 The geometry of the universe
FINALS



05/13
FINAL EXAM (8:00-10:00)


Check other important dates on the Academic Calendar



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