Introduction to topology

18.901: Introduction to topology (Fall 2023)

The syllabus for this course is available here.

Lecture time: Tuesday and Thursday: 2:30 pm - 4:00 pm

Location: 2-105

Instructor Email: pieloch@mit.edu
Instructor Office Hours: See Canvas announcements


Problem Sets

  • Problem set 5
    Students are not required to turn in this homework.








Exams

  • Midterm 1:
    • Time: Thursday, October 5th, 2023 at 2:30 pm - 4:00 pm
    • Material covered: Lectures 1-8, but you will not be responsible for knowing the proofs of Urysohn's lemma and metrization theorem.
    • Midterm 1, Midterm 1 Solutions

  • Midterm 2:
  • Final exam:
    • Time: Wednesday, December 20th, 2023 at 9:00 am - 12:00 pm
    • Material covered: Lectures 1-24.




Course Schedule

This section will be updated after class to list the material that was covered along with the lecture notes. Suggested reading that relates to the material covered in class will also be posted. For a tentative schedule of the course, see the syllabus.

  • Week 1
    • September 7th, 2023:
      • Introduction, topological spaces, bases, interiors, closures, limit points
      • Munkres 12, 13, 17 (ignore Hausdorff discussion)
      • Lecture 1 notes

  • Week 2
    • September 12th, 2023:
      • Metric spaces, subspaces, product spaces, quotient spaces.
      • Munkres 15, 16, 19, 20, 21. Munkres 3 covers equivalence relations.
      • Lecture 2 notes
    • September 14th, 2023:

  • Week 3
    • September 19th, 2023:
      • Limits and continuity, (path)-connectedness.
      • Munkres 23, 24.
      • Lecture 4 notes
    • September 21th, 2023:

  • Week 4
    • September 26th, 2023:
      • Compactness, Hausdorff space.
      • Munkres 17 (the subsection on Hausdorff spaces), 26, 28.
      • Lecture 6 notes
    • September 28th, 2023:

  • Week 5
    • October 3rd, 2023:
      • Urysohn's lemma, Urysohn's metrization theorem, review.
      • Munkres 34, 35.
      • Lecture 8 notes
    • October 5th, 2023:
      • In-class exam - Midterm 1

  • Week 6
    • October 10th, 2023:
      • No class
    • October 12th, 2023:

  • Week 7
    • October 17th, 2023:
      • Manifolds, paracompactness, covering dimension.
      • Munkres 36, 39, 41, 50
      • Lecture 10 notes
    • October 17th, 2023:
      • More covering dimension, Baire's theorem, embeddings of compact metric spaces.
      • Munkres 48, 50
      • Lecture 11 notes

  • Week 8
    • October 24th, 2023:
    • October 26th, 2023:

  • Week 9
    • October 31st, 2023:
    • November 2nd, 2023:
      • More groups, definition of fundamental group
      • Artin chapter 2, Hatcher section 1.1
      • Lecture 15 notes

  • Week 10
    • November 7th, 2023:
      • Fundamental groups, change-of-basepoint, induced homomorphisms
      • Hatcher section 1.1
      • Lecture 16 notes
    • November 9th, 2023:

  • Week 11
    • November 14th, 2023:
      • In-class exam - Midterm 2
    • November 16th, 2023:
      • The fundamental theorem of algebra, free groups
      • Hatcher section 1.1, 1.2
      • Lecture 18 notes

  • Week 12
    • November 21st, 2023:
    • November 23rd, 2023:
      • No class

  • Week 13
    • November 28th, 2023:
    • November 30th, 2023:

  • Week 14
    • December 5th, 2023:
    • December 7th, 2023:

  • Week 15