MMA100 Topology Spring 23

Welcome to the course of Topology!   

 

This page contains the program of the course.   Below are the weekly plan for lectures and exercise sessions (to be continuously updated).   

Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

 

All lectures and exercise sessions will be held on campus.

 

Schedule:  lectures - Tuesday and Wednesday at 15.15,  MVF31  

                   exercise sessions - Friday at 13.15, MVF26.

 

Weekly plan for lectures 

(subject to change)

 

Week 1 Lecture Tuesday

Brief overview. Sections 12 and 13. 

 

Lecture Wednesday

Sections 15, 16.

 

Week 2 Lecture 1

Sections 17, 18.

Lecture 2

Sections 19, 20.

Week 3 Lecture 1

 Section 23 and a part of 24

Lecture 2

Section 24 (the rest of), a part of section 25 (if time permits), and a part of 26. 

Week 4 Lecture 1

The rest of section 26; section 27, 28.

Lecture 2

Sections 43, 44. 

Week 5 Lecture 1

(Parts of) sections 30, 31, 32. Section 33. 

Lecture 2

Sections 34, 35 and a part of section 20 needed for Urysohn metrization theorem. 

Week 6 Lecture 1

Sections 51, 52

Lecture 2

a proof that sphere is simply connected (different from the one in the book), a part of section 54, a part of section 55

Week 7 Lecture 1

 section 55, a part of section 58 (about homotopy equivalence),  section 22 

Lecture 2

examples of surfaces (from section  60);  classification of surfaces ( parts of sections 74, 76, 77)  

Week 8 Lecture Discussion of solutions for exam for 2021. exam2021 (1).pdf 

 

Recommended exercises

 

Week 1

 Ch. 2  Section 13:  1, 3, 4, 7 (excluding R_K), 8.   Section 16:  2, 3, 4, 5.

 

Week 2

ExercisesWeek2-1.pdf   + 1 more problem: prove that for a function on the real line  the "epsilon-delta"-definition of continuity coincides with the definition of continuity in Topology

 

To get used to work with images/preimages you can do  Ch.1 Section 2: 2, 3, 4. These exercises we will not discuss at exercises session unless anybody would ask about it. 

Week 3

ExercisesWeek3-1.pdf 

Week 4

ExercisesWeek4-1.pdf 

Week 5

ExercisesWeek5-2.pdf 

Week 6

ExercisesWeek6b(2023).pdf 

Week 7

ExercisesWeek7-1.pdf 

 

 

 

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