226 Gray Hall

michaelr at american {dot} edu

Office hours: Monday 1-2pm; Tuesday 6-6:30pm; Wednesday 9:30am-10:15am and 1-2pm; Thursday 9:30am-10:15am, 1-2pm, and 6-6:30pm, or by appointment (please contact me 24 hours in advance to make arrangements)

My research website http://www.drmichaelrobinson.net/

Feel free to contact me with any questions (course-related or not)

Homework assignments

Course schedule

Concerning programming in this course

Information about exams

Some useful links

Course policies

Prerequisite: MATH-503 or my permission. Conveniently, Chapter 0 of the textbook is a great resource for what you will typically need to remember!

The course textbook is *Introduction to General Topology*, by George L. Cain.

In this course, students will

- Learn the definitions and key facts about topological spaces and continuous functions,
- Learn to classify spaces and functions according to topological properties,
- Develop comfort in using topological ideas outside of topology, and
- Continue to develop the skill of reading and writing mathematical proofs.

Homework 1 due Tuesday, September 10

Homework 2 due Tuesday, September 24

Homework 3 due Tuesday, October 8

Homework 4 due Tuesday, October 22

Homework 5 due Tuesday, November 7

Homework 6 due Tuesday, November 21

Homework 7 due Tuesday, December 5

- Recite the definition of a topology and explain the topology of familiar spaces, such as the real line and the sphere
- Identify situations where non-Euclidean topologies are helpful
- Prove basic facts about how open and closed sets can be used to represent a topology

August 27: Abstract simplicial complexes

August 29: Sections 0.1-0.5: Sets, functions, relations, and the integers

September 3: Section 1.1: Pseudometrics

September 5: Section 1.2: Open and closed sets

September 10: Section 2.1: Topological spaces

September 12: Section 2.1: Topological spaces

September 17: Section 2.2: Topological bases

September 19: Section 2.3: Subspaces

September 24: Section 2.3: Subspaces

September 26: Exam 1

- Recite both standard definitions of continuity for functions,
- Give examples and nonexamples of continuous functions between two topological spaces,
- Explain how continuous functions can be used to compare topologies, and
- Perform this comparison on some common topological spaces

October 1: Section 3.1: Continuity

October 3: Section 3.1: Continuity

October 8: Section 3.2: Homeomorphisms

October 10: Homotopies

October 15: Section 3.3: The weak topology

October 17: Section 10.1: The strong (quotient) topology

October 22: CW complexes

October 24: Exam 2

- Recite and explain the definitions of connectness and compactness
- Explain why compactness has the name it does
- Explain how to use connectedness and compactness to distinguish two different topological spaces

October 29: Section 4.1: Connectedness

October 31: Section 4.1: Connectedness

November 5: Section 4.2: Connected components

November 7: Section 4.3: Path connectedness

November 12: Section 4.4: Local path connectedness

November 14: Section 5.1: Compactness

November 19: Section 5.1: Compactness

November 21: Section 5.2: One-point compactification

December 3: Applications!

December 5: Review for the final

**Final exam: December 12, 5:30pm-8:00pm**

25% Homework

25% Exam 1

25% Exam 2

25% Final exam

Late homeworks will not be accepted, unless there is an official (University-approved) reason for doing so.