MATS214 Topology (4 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023
Description
Topological spaces, relative topology, product topology, metrizable spaces, compact topological spaces
Learning outcomes
After passing the course the student:
- knows the concepts of a topological space, Hausdorff space, relative topology, product topology, and compact space
- know the Baire theorem and its applications
- can apply methods and proofs of the course to various problems
- has deepened his/her abilities to understand course related concepts in applications
Description of prerequisites
Introduction to mathematical analysis 2, Vector analysis 1 and 2, Metric spaces
Study materials
Applicable parts of J. Väisälä: Topology 2
J. Munkres: Topology (2nd ed.)
Literature
- J. Munkres: Topology (2nd ed.)
- S. Willard: General topology
Completion methods
Method 1
Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 2
Select all marked parts
Method 2
Evaluation criteria:
Final exam.
Select all marked parts
Parts of the completion methods
x
Teaching (4 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Hyväksyttyyn suoritukseen vaaditaan riittävä määrä pisteitä kurssitentistä ja laskuharjoitusten hyvityspisteistä.
Language:
English, Finnish
Study methods:
Lectures and homework exercises
Teaching
10/28–12/18/2020 Lectures
12/16–12/16/2020 Exam
1/13–1/13/2021 Exam
x
Exam (4 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Hyväksyttyyn suoritukseen vaaditaan riittävä pistemäärä lopputentissä.
Language:
English, Finnish
Study methods:
Independent study and final exam.