Math 3110/4110 – Topology

Lecture Time: 2:00pm – 3:50pm (TR) Location: Knudson Hall 100

Textbook: Willard, General Topology

Prerequisite: Math 3161

Instructor: Mei Yin   mei.yin@du.edu
   Office and Office Hours: Zoom, 10:30am – 12:00pm (TR), or by appointment

Course Description: Point set topology including topological spaces, connectedness, compactness and separation axioms; preparation for advanced courses in analysis.

Learning Objectives: By the end of the course, you should be able to:
1. Give several examples of topological spaces.
2. Describe the topologies using open sets, or closed sets, or using neighborhoods, or bases.
3. State and prove many characterizations of continuous functions between topological spaces.
4. Use functions to construct new topological spaces (quotients and products).
5. Prove separation and countability properties for topological spaces and use these properties to distinguish them.
6. Understand the limitations of using sequences to describe some topologies and the need to use filters and nets in the general case.
7. Understand the definition of compactness and recognize compact spaces in many topological settings.
8. State and prove results about compact spaces, including Tychonoff Theorem.
9. Understand the definition of connectedness and recognize connected spaces in many topological settings.

Tentative Calendar:

The Week Of
 Material Covered
March 27 – March 31
 Introduction, Topological Spaces
April 3 – April 7
 Closure, Interior, Neighborhoods, Bases, Subbases
April 10 – April 14
 Subspace Topology, Continuous Functions, Weak Topology
April 17 – April 21
 Product Topology, Quotient Topology, Separation Axioms (I)
April 24 – April 28
 Product Topology, Quotient Topology, Separation Axioms (II)
May 1 – May 5
 Filters, Ultrafilters, Nets
May 8 – May 12
 Compactness, Tychonoff Theorem (I)
May 15 – May 19
 Compactness, Tychonoff Theorem (II)
May 22 – May 26
 Connectedness
May 30 – June 2
 Complete Metric Spaces, Baire Theorem

Grading: Your final grade for the course will be determined based on a numerical weighted average calculated as follows: Attendance/Participation 20% Quizzes 40% Final Exam 40%. This average percentage will then be converted into a final letter grade based partially on how other students perform this quarter, and partially on typical percentage grades from previous quarters of the course.

Students are expected to attend and actively participate in every scheduled class.

Homework will be assigned about once a week and is for students' review and practice only. Homework will not be collected and is not included in the computation of your grade.

There will be a biweekly quiz on Thursdays in class during weeks 2, 4, 6, 8, and 10. Quiz problems will be based on class lectures and assigned homework. Each quiz will account for 10 points; the lowest quiz score will be dropped. Makeup quizzes will only be offered in the event of extreme circumstances. If you think you have a problem which will force you to miss a quiz, please come talk to me as soon as possible.

There will be a cumulative final exam on Tuesday, June 6, 2-3:50pm.

Help: Additional handouts will be distributed throughout the quarter. Students are also encouraged to ask for individualized help from the instructor at any time.

Students with Disabilities: If you qualify for academic accommodations because of a disability or medical issue, please submit a faculty letter to me from Disability Services Program (DSP) in a timely manner so that your needs may be addressed. DSP determines accommodations based on documented disabilities/medical issues. DSP is located on the 4th floor of Ruffatto Hall, 1999 E Evans Ave, 303-871-2278. Information is also available online at http://www.du.edu/disability/dsp; see the Handbook for Students with Disabilities.

Honor Code: Follow the Honor Code in all activities related to this course. Incidents of academic misconduct will be reported to and investigated by the Office of Student Conduct.

Inclusive Learning Environment: In this class, we will work together to develop a learning community that is inclusive and respectful. Our diversity may be reflected by differences in race, culture, age, religion, sexual orientation, socioeconomic background, and myriad other social identities and life experiences. The goal of inclusiveness, in a diverse community, encourages and appreciates expressions of different ideas, opinions, and beliefs, so that conversations and interactions that could potentially be divisive turn instead into opportunities for intellectual and personal enrichment.

A dedication to inclusiveness requires respecting what others say, their right to say it, and the thoughtful consideration of others' communication. Both speaking up and listening are valuable tools for furthering thoughtful, enlightening dialogue. Respecting one another's individual differences is critical in transforming a collection of diverse individuals into an inclusive, collaborative and excellent learning community. Our core commitment shapes our core expectation for behavior inside and outside of the classroom.

Religious Accommodations: University policy grants students excused absences from class or other organized activities for observance of religious holy days, unless the accommodation would create an undue hardship. Faculty are asked to be responsive to requests when students contact them in advance to request such an excused absence. Students are responsible for completing assignments given during their absence, but should be given an opportunity to make up work missed because of religious observance. Once a student has registered for a class, the student is expected to examine the course syllabus for potential conflicts with holy days and to notify the instructor by the end of the first week of classes of any conflicts that may require an absence (including any required additional preparation/travel time). The student is also expected to remind the faculty member in advance of the missed class, and to make arrangements in advance (with the faculty member) to make up any missed work or in-class material within a reasonable amount of time.

Other: Check the DU academic calendar for important dates throughout the quarter: http://www.du.edu/registrar/calendar/index.html.