Introduction to topology

18.901: Introduction to topology (Spring 2025)

The syllabus for this course is available here.

Lecture time: Tuesday and Thursday: 1:00 pm - 2:30 pm

Location: 2-190

Instructor Email: pieloch@mit.edu
Instructor Office Hours: TBD

Problem Sets

• Problem set 1
  Due Thursday, February 6th, 2025 at 11:59 am.
  
  

• Problem set 2
  Due Thursday, February 13th, 2025 at 11:59 am.
  
  

• Problem set 3
  Due Thursday, February 20th, 2025 at 11:59 am.
  
  

• Problem set 4
  Due Thursday, February 27th, 2025 at 11:59 am.
  
  

• Problem set 5
  This assignment is not due, will not be graded, and should not be turned in.
  
  

• Problem set 6
  Due Thursday, March 13th, 2025 at 11:59 am.
  
  

• Problem set 7
  Due Thursday, March 20th, 2025 at 11:59 am.
  
  

• Problem set 8
  Due Thursday, April 3rd, 2025 at 11:59 am.
  
  

• Problem set 9
  Due Thursday, April 10th, 2025 at 11:59 am.
  
  

Exams

• Midterm 1:
  • Time: Thursday, March 6th, 2025 at 1:00 pm - 2:30 pm
  • Material covered: Lectures 1-8
  • Blank Midterm 1, Solutions to Midterm 1
  
  
• Midterm 2:
  • Time: Thursday, April 17th, 2025 at 1:00 pm - 2:30 pm
  • Material covered: TBD
  
  
• Final exam:
  • Time: TBD
  • Material covered: TBD
  
  

Course Schedule

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

• Week 1
  • February 4th, 2025:
    • Introduction, topological spaces, bases, interiors, closures, limit points
    • Lecture notes: 1.1, 1.2
  • February 6th, 2025:
    • Dense subsets, metric spaces, subspaces, product spaces
    • Lecture notes: 1.2, 1.3
  
  
• Week 2
  • February 11th, 2025:
    • Quotient topology, continuous maps
    • Lecture notes: 1.3.4, 1.4
  • February 13th, 2025:
    • Continuous maps, limit points
    • Lecture notes: 1.4
  
  
• Week 3
  • February 18th, 2025:
    • No class
  • February 20th, 2025:
    • Connectedness
    • Lecture notes: 1.5
  
  
• Week 4
  • February 25th, 2025:
    • Compactness, Hausdorff spaces
    • Lecture notes: 1.6, 1.7
  • February 20th, 2025:
    • Normal spaces
    • Lecture notes: 1.8.1
  
  
• Week 5
  • March 4th, 2025:
    • Urysohn's lemma, Urysohn's metrization theorem
    • Lecture notes: 1.8.2
  • March 6th, 2025:
    • Midterm 1
  
  
• Week 6
  • March 11th, 2025:
    • Manifolds
    • Lecture notes: 2.1
  • March 13th, 2025:
    • Paracompactness
    • Lecture notes: 2.2
  
  
• Week 7
  • March 18th, 2025:
    • Covering dimension, metric space embedding theorem
    • Lecture notes: 2.3, 2.4
  • March 20th, 2025:
    • Manifold embedding theorem, Homotopy
    • Lecture notes: 2.4, 3.1
  
  
• Week 8
  • March 25th, 2025:
    • No class
  • March 27th, 2025:
    • No class
  
  
• Week 9
  • April 1st, 2025:
    • Groups, subgroups, homomorphisms
    • Lecture notes: 4.1.1, 4.1.2, 4.1.3
  • April 3rd, 2025:
    • Normal subgroups, quotient groups, definition of fundamental group
    • Lecture notes: 4.1.4, 3.2