Math 121:  Introduction to Topology


In this course we introduce the basic notions in topology.

Instructor: Ko Honda

  • Office: MS 7919
  • E-mail: lastname at math dot ucla dot edu 
  • URL:
  • Office hours: M 11-11:50 am, W 1-1:50 pm

TA: Ben Spitz (benspitz at math dot ucla dot edu); office hours TBA

Class Meetings: Every week there will be three hours of lecture as well as one hour of discussion.  (The first two weeks will be remote.)

  • Lectures:  MWF 2-2:50 pm @ MS 5147
  • Discussion section:  Th 2-2:50 pm @ MS 5147

COVID-19 Policy:

Keeping our community safe depends on each of us following the latest UCLA health and safety guidelines. Things might change, but for the moment you:

  • Are responsible, regardless of vaccination status, for wearing an approved mask that fully covers our nose and mouth for the duration of class, office hours, or other course-related activity.  Disposable masks are available at the Wooden Center for anyone unable to obtain a mask or who has forgotten to bring one to campus.  Appropriate masks include two-ply woven fabric masks, surgical masks, non-woven KN95 masks, and N95 respirators. Please note that scarves, balaclavas/ski masks, single-layer fabric masks and neck gaiters, bandanas, and turtleneck collars are not adequate. For those that have a medical reason not to wear a mask, you can contact the Center for Accessible Education (CAE) to have this exception approved and sent to instructors.
  • Must be fully vaccinated or have submitted an exception request.  Unvaccinated students with pending or approved exceptions must comply with twice-weekly testing.
  • Are required to complete daily symptom checks prior to coming to campus, regardless of vaccination status, and must stay home if you are not cleared by the symptom survey and/or are advised by the Exposure Management Team to quarantine or isolate.
  • Will refrain from eating or drinking in the classroom. If you need to take a sip of water or eat something quickly for medical reasons, please step outside the room to do so.

Please stay home if sick or potentially exposed. Email me if you need to stay home, and we will arrange for you to access class recordings/notes.

The flip side of this requirement is that I also cannot come in even if I have mild cold symptoms such as a headache, runny nose, or sore throat.  I think it's likely this will happen at some point in the quarter because I catch colds pretty often.  In that case I'll email everyone in the class and we'll have to switch to Zoom for a lecture or two.

Be advised that refusal to comply with current campus directives related to COVID-19 mitigation will result in dismissal from the classroom and referral to the Office of Student Conduct. If you have any questions or concerns about UCLA’s COVID-19 protocol, go to


  1. Metric and topological spaces
  2. Completeness, compactness, connectedness, continuity
  3. Fundamental group, covering spaces, applications
Textbook: Gamelin and Greene, Introduction to Topology, 2nd Ed., Dover

Prerequisite: Math 131A or equivalent

REQUIREMENTS:  You are responsible for carefully reading the following and being aware of all the requirements.  Please ask questions about anything you don't understand.

Classroom Expectations

I want you to enjoy this class, but please respect my right to teach and your classmates' rights to learn.
  • Please refrain from disruptive behavior (such as unnecessary talking).
  • Laptop/tablet use is restricted to taking notes.  Your cell phones must be turned off (this in particular means you cannot use your cell phones in class).  Also no reading newspapers and other non-class materials.
Grading System
  • Weekly HW: 25%
  • Midterm: 25%
  • Final Exam: 50%
Homework: HW assigned each week will be due by the end of the following Monday, on Gradescope.  For example, the HW assigned on Mon 1/3, Wed 1/5, and Fri 1/7 are due on Mon 1/10.  See the class schedule.
  • We will NOT grade the entire HW; rather a subset of the HW will be chosen and graded. 
  • You may work with others, consult other textbooks, and look up resources online (although I don't recommend it) but the HW you turn in must be written by you, in your own words, and you must cite your sources used and your collaborators. Any HW without proper attribution or not written in your own words will be considered plagiarized and will automatically receive a 0, and you may be subject to disciplinary action depending on the severity of the infraction.
  • Please pay attention to your writing:  The solutions you submit must be clean (i.e., no rambling discussions and the logical order should be clear) and complete.  Even if you have the right idea, if we do not understand what you write, points will be taken off.

Midterms:  There will be one in-class midterm exam during the quarter (Monday, February 7).  No makeup midterms will be given.  Any absence on a midterm will result in a score of 0, unless excused.  In case of an excused absence, the final exam grade will replace the midterm grade that is missed.  It is your responsibility to let me know in advance if you will be absent for a legitimate reason, so I can excuse you.  In case of an emergency (e.g., sudden illness), please supply some documentation afterwards (e.g., doctor's note).  If you have any conflicts with the midterm, please come talk to me about it within the first two weeks of class.

Final Exam:  Thursday 3/17, 3pm-6pm

Academic Integrity
The instructor strongly adheres to the University policies regarding academic integrity violations, and will strictly enforce these rules. You are encouraged to review the UCLA Student Conduct Code.

Students with Disabilities 

Any student requesting academic accommodations based on a disability is required to register with the Center for Accessible Education (CAE).

WARNING:  The course syllabus provides a general plan for the course; deviations may become necessary. 

Last modified:  January 4, 2022.