MA 564. Introduction to Topology

General Information

• Time: Tue. & Thu. 11:00 AM - 12:15 PM

• Place: EPC 208

• Prerequisite: MA 225, 230 and MA 511.

• Textbook: Y. Gamelin and R. Greene, Introduction to Topology, 2nd edition, Dover, ISBN. 9780486406800

• Course description

• Syllabus
  
  
  

Instructor: Yoosik Kim

• Email: yoosik (at) bu (dot) edu

• Office hours (MCS 237B): Mon. 3 PM - 5 PM, Fri. 10 AM - 11 AM, or by appointment
  
  
  

Homework

• Homework 1 (Jan. 25th, Due on Feb. 5th) - Solutions (of selected problems)

• Homework 2 (Feb. 1st, Due on Feb. 12th) - Solutions (of selected problems)

• Homework 3 (Feb. 8th, Due on Feb. 21st) - Solutions (of selected problems)

• Homework 4 (Feb. 15th, Due on Feb. 26th) - Solutions (of selected problems)

• Homework 5 (Feb. 22th, Due on Mar. 5th) - Solutions (of selected problems)

• Homework 6 (Mar. 7th, Due on Mar. 26th) - Solutions (of selected problems)

• Homework 7 (Mar. 22nd, Due on Apr. 2nd) - Solutions (of selected problems)

• Homework 8 (Mar. 29th, Due on Apr. 9th) - Solutions (of selected problems)

• Homework 9 (Apr. 5th, Due on Apr. 16th) - Solutions (of selected problems)

• Homework 10 (Apr. 12th, Due on Apr. 23th) - Solutions (of selected problems)

• Homework 11 (Apr. 19th, Due on Apr. 30th) - Solutions (of selected problems)
  
  
  

Lecture notes - The handwritten notes might be incomplete.

• What is Topology?

• Metric spaces

• Topological spaces

• Subspace topology

• Base for topology

• Continuous functions

• Countability, Separation axioms

• (Finite) Product Spaces

• Compactness

• Connectedness

• Path Connectedness

• Quotient Spaces

• Product spaces

• Compactness in metric spaces

• Uryshon's Lemma

• Groups

• Homotopic paths

• Fundamental groups

• Induced homomorphisms

• Covering spaces

• Applications of the index

• Homotopy equivalence
  
  
  

Exams

• The midterm exam (Mar 5th - Mar. 7th) - Problems, Solutions

• The final exam (May 2nd - May 8th) - Problems, Solutions