Schedule

Review before classes start: Basic Set Theory and Logic. (Self-study)

  • Videos covering this background prerequisite material are posted in the course Blackboard website learning modules under Week 0.

Week of Jan 17

  • Note: First class on Wednesday, Jan 17

  • Topics:

  • Chapter 1, Munkres + Handouts.

    • Set Theory notation
    • Basic Logic

Week of Jan 22

  • Homework 1 Due Saturday, Jan 27, 11:59PM

  • Topics:

  • Chapter 2, Munkres: Sections 12.

    • Ordered Sets
    • Topological spaces

Week of Jan 29

  • Homework 2 Due Saturday, Feb 3, 11:59PM

  • Topics:

  • Chapter 2, Munkres: Sections 13, 14, 15, 16.

    • Basis for Topologies
    • Order Topologies
    • Product Topologies
    • Subspace Topologies

Week of Feb 5

  • Homework 3 Due Saturday, Feb 10, 11:59PM

  • Topics:
  • Chapter 2, Munkres: Section 17, 18.
    • Closed sets and limits points
    • Hausdorff spaces
    • Continuous functions

Week of Feb 12

  • Homework 4 Due Saturday, Feb 17, 11:59PM

  • Topics:
  • Chapter 2, Munkres: Section 18, 19.
    • Continuous functions
    • Homeomorphisms
    • Topologies on infinite product spaces

Week of Feb 19

  • Homework 5 Due Saturday, Feb 24, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Section 20.
    • Metric spaces, Part 1.

Week of Feb 26

  • Homework 6 Due Saturday, March 2, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Section 21.
    • Metric spaces, Part 2.

Week of March 4

The midterm will be on Wed, March 6, 7:30-9PM (Rochester night) in TBA.

  • Topics:
  • Chapter 2: Supplement, Handouts.
    • Topological Manifolds
    • Smooth Manifolds

SPRING BREAK IS MARCH 9 THROUGH MARCH 17. Classes resume Monday, March 18.


Week of March 18

  • Homework 7 Due Saturday, March 23, 11:59PM

  • Topics:
  • Chapter 2, Munkres: Sections 22.
    • Groups
    • Topological Groups
    • Lie groups

Week of March 25

  • Homework 8 Due Saturday, March 30, 11:59PM

  • Topics:
  • Chapter 2, Munkres: Sections 22. Handouts.
    • Quotient Topology and Quotient Constructions
    • Mobius band, Torus, Klein Bottle, Projective spaces.

Week of April 1

  • Homework 9 Due Saturday, April 6, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Sections 23, 24, 25.
    • Connected Spaces.
    • Connected Subspaces of the Real Line.
    • Components and Path Components

Week of April 8

  • Homework 10 Due Saturday, April 13, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Sections 26, 27.
    • Compact Spaces.
    • Compact Subspaces of the Real Line.

Week of April 15

  • Homework 11 Due Saturday, April 20, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Sections 28, 29(skim).
    • Classification of compact, connected surfaces.
    • Limit Point and Sequential Compactness.
    • Local Compactness.

Week of April 22

  • Homework 12 Due Saturday, April 27, 11:59PM

  • Topics:
  • Chapter 3, Munkres: Sections 30-33.
    • Countability and Separation Axioms.
    • Normal Spaces.
    • Urysohn’s Lemma.

Week of April 29

  • Topics:
  • Assorted final topics.

Monday, April 29 is the last day of class.


FINAL

The final will be on Monday, May 6, 8:30-11:30 AM (Rochester morning) in Gavett 310.