### MA 231: Topology

#### August 2022

### Syllabus

Open and closed sets, continuous functions, Metric topology, Product topology, Connectedness and path-connectedness, Compactness, Countability axioms, Separation axioms, Complete metric spaces, Quotient topology, Topological groups, Orbit spaces, Urysohn’s lemma, Metrizability, Baire Category theorem.

#### Suggested books:

- Armstrong, M. A., Basic Topology, Springer (India), 2004.
- Munkres, J. R., Topology, Pearson Education, 2005.
- Viro, O.Ya., Ivanov, O.A., Netsvetaev, N., and Kharlamov, V.M., Elementary Topology: Problem Textbook, AMS, 2008.

We will mostly follow the book **Elementary Topology: Problem Textbook** by **Viro et. al.**, which is available online.

#### Assignments

Assignments will be posted roughly once a week.

- Topological Spaces due by Thursday, Aug 18, 2022.
- Bases due by Thursday, Aug 25, 2022.
- Metric Spaces due by Thursday, Sep 8, 2022.
- Subsets and Continuity due by Thursday, Sep 15, 2022.

#### Course Details

**Instructor:**Siddhartha Gadgil**E-mail:***siddhartha.gadgil@gmail.com***Office:**N-15, Department of Mathematics, IISc.**Timing:**Mon, Wed, Fri 9:00 am - 10:00 am.**Venue:**LH-4.**Teaching Assistant:**Srijan Sarkar**Office:**X-13, Department of Mathematics, IISc.**Tutorial timing:**Wed 5:00 pm - 6:00 pm**Microsoft Teams:**Please join the Team “Topology : August 2022” using the Team code j0irp36

##### Additional Resources

This course was taught online in 2021. The lectures are online as are the whiteboards. If you want to printout the whiteboards, please use the compact version.

Note that students are responsible for all the material covered in the lectures this semester, which is likely to be more than that in the above resources. Experience also suggests that offline lectures are more effective. Thus, it is wise to use the above as supplements, not substitutes, for the lectures.

#### Examinations and Grades

Grades will be based on the assignments, midterm examination and final examinations with the following weightages.

**Assignments:**10%**Midterm:**40%**Final exam:**50%

##### Midterm

The following are the details for the Midterm Examination

**Date:**Monday, September 19, 2021.**Timing:**9:00 am to 10:30 am.**Venue:**LH-4, Department of Mathematics.**Syllabus**: Material covered in lectures up to September 12, 2022.**Weightage:**40% of the total.