Math 351: Elementary Topology I

Section 4, Fall 2012

Prof. Bert Guillou


email: bertguillou uky edu
Phone: (859) 257-4781
Office: 773 POT
Office Hours: Monday, 10-11 and 3-4.
Extra Credit Project:
A list of problems can be turned in at the final exam for extra credit.




Schedule


Assignment Date
Lecture 1: Introduction, 0.4. Aug. 22
Lecture 2: Open sets in Rn: 0.4. Aug. 24
Lecture 3: Closed sets in Rn, Topological spaces: 0.4, 1.1. Aug. 27
Lecture 4: Topological spaces, examples of topologies on R, injections/surjections/bijections: 0.6, 1.1.
HW1 due
Aug. 29
Lecture 5: Finite/infinite/countable sets, the cofinite topology on R: 0.6, 1.1, 1.2. Aug. 31
Lecture 6: Reviewed HW1, examples of bases Sept. 5
Lecture 7: Generating a topology from a basis
HW2 due
Sept. 7
Lecture 8: Reviewed HW2 Sept. 10
Lecture 9: Hausdorff spaces, closures, and interiors
HW3 due
Sept. 12
Lecture 10: Reviewed HW3, examples of closure and interior Sept. 14
Lecture 11: Boundaries, limits of sequences Sept. 17
Lecture 12: Limits of sequences, Worksheet
HW4 due
Sept. 19
Lecture 13: Reviewed HW4, Accumulation points Sept. 21
Lecture 14: Reviewed WS1, Subspaces Sept. 24
Lecture 15: Subspaces, Worksheet and Solutions
HW5 due
Sept. 26
Lecture 16: Reviewed HW5, Continuous functions Sept. 28
Lecture 17: Continuous functions Oct. 1
Lecture 18: Continuous functions, Worksheet and Solutions
HW6 due
Oct. 3
Lecture 19: Reviewed HW6, Continuous functions Oct. 5
Review Worksheet and Solutions Oct. 8
Exam review Oct. 10
Exam 1. Letter grades Oct. 12, in class
Lecture 20: Reviewed Exam 1, Homeomorphisms Oct. 15
Lecture 21: Homeomorphisms Oct. 17
Lecture 22: Product topology, Worksheet and Solutions
HW7 due (Optional)
Oct. 19
Lecture 23: Reviewed WS5, Examples of products Oct. 22
Lecture 24: Embeddings of the torus and cylinder,
Worksheet and Solutions
HW8 due
Oct. 24
Lecture 25: Reviewed HW8 and WS6, Examples of quotients Oct. 26
Lecture 26: Quotient topology Oct. 29
Lecture 27: General quotient topology, Worksheet Oct. 31
Lecture 28: Reviewed HW9 and WS7
HW9 due
Nov. 2
Lecture 29: Quotients: the torus, the Klein bottle, and RP2 Nov. 5
Lecture 30: Unions, connected sums Nov. 7
Review worksheet and Solutions
HW10 due
Nov. 9
Exam review Now. 12
Exam 2 Letter grades Nov. 14, in class
Lecture 31: Metric spaces Nov. 16
Lecture 32: Properties of metric spaces Nov. 19
Lecture 33: Connectedness Nov. 26
Lecture 34: Connectedness of products, IVT
Worksheet and Solutions
HW11 due
Nov. 28
Lecture 35: Compactness
Test corrections due
Nov. 30
Lecture 36: Compactness of [a,b] Dec. 3
Lecture 37: Heine-Borel Theorem, IVT
Worksheet and Solutions
Dec. 5
Review worksheet Dec. 7
FINAL EXAM!! Dec 12, 1:00 PM



Department of Mathematics