Topology 20

Every lesson provides a list of exercises, students that intend to have credits from the course are expected to solve a certain amount of them, which depends on the specific exercise sheet. The exercises are a necessary and sufficient condition to be admitted to the oral exam, but do not provide credits per se. Solutions can be sent by email or brought brevi manu the week after.

• 1. What is a geometric object?

• 2. Bestiary.

• 3. Separation axioms + : Separation axioms by Vipul Naik.

• 4. Compactness.

• 5. Connectedness.

• 6. Bonus track I: topological groups.

• 7. Writing down maps.

• 8. Actions.

• 9. Coverings.

• 10. Using coverings.

• 11. Van Kampen + : A proof of weak Van Kampen by Munkres.

• 12. Bonus track II: open mic.

Syllabus of the course :

• the intersection between the notes of prof. Lukáš Vokřínek (see his webpage and click on Topologie) and the standard syllabus.

• the notes in this webpage. Some of exercises that were given during the semester might be asked during the examination. If an auxiliary book is needed for my notes, I suggest the book by Munkres.

: Topology by James R. Munkres. : Elementary Topology Problem Textbook by Viro, Ivanov, Netsvetaev and Kharlamov.

If you send me an email about this course make sure to include the word MUNITOP20 in the subject. This makes my life easier.

Rules for the exam : The last exercise sheet should be sent at the latest on the 15th of May. If you plan to do the exam before that day, you should send the last exercise sheet at least 3 days before the exam. If needed, a delay of 5 days will be tolerated, but must be agreed via email. The exams will be contactless, using Zoom. They will take place from the middle of May untill the end of September. The dates will be announced gradually and will reflect your wishes.