Topologie
6 EC
Semester 2, period 4, 5
5122TOPO6Y
In this course the fundamentals of topology are treated. Various concepts that play a role in the analysis are reflected in this course in abstract form. In this course we lay a foundation for the further study of geometry, algebraic topology and differential topology. Topics covered are topological spaces, continuous maps and homeomorphisms, connectedness, compactness, and quotient spaces. The fundamental group will be discussed in detail. We calculate the fundamental group of a number of known spaces and study the relationship between fundamental groups and covering spaces.
Additional materials provided on Canvas
Activiteit | Aantal uur |
Hoorcollege | 30 |
Tentamen | 3 |
Tussentoets | 3 |
Werkcollege | 28 |
Zelfstudie | 104 |
Programme's requirements concerning attendance (OER-B):
Additional requirements for this course:
Aanwezigheid bij de werkcolleges is verplicht. Als je niet bij minstens 80% van de werkcolleges aanwezig bent geweest dan vervalt je recht op het hertentamen, zoals vermeldt in het OER-B artikel 4.9 lid 2.
Item and weight | Details |
Final grade | |
1 (100%) Deeltoets |
The midterm test covers point-set topology and counts for 25%
The Final Exam covers both point-set topology and algebraic topology and counts for 60%
The homework counts for 15%
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
Here is a tentative overview of the course with the corresponding sections from the text by Munkres that will be covered.
Week 1: Topological spaces, examples of topological spaces, basis for a topology, relationship with metric spaces (sections 12, 13, 20).
Week 2: Product topology, subspace topology, interior and closure (sections 15,16,17).
Week 3: Hausdorff spaces, continuous functions (sections 17 and 18).
Week 4: Connected spaces (sections 23, 24, 25)
Week 5: Compactness (sections 26, 27).
Week 6 Quotient topology (section 22).
Week 7: Review
Week 8: Midterm test
Week 9: Homotopy of continuous images and of paths (section 51).
Week 10: The Fundamental Group and Cover Spaces (sections 52 and 53).
Week 11: The fundamental group of the circle (section 54).
Week 12: Retractions (section 55)
Week 13: Homotopy type and deformations (section 58).
Week 14: The fundamental group of some surfaces (sections 59 and 60).
Week 15: Review
There is an honors extension worth 3 EC for the Topology course.
In the Honors extension, students will apply surface classification themselves.