MATS214 Topology (4 cr)

Open the course unit brochure on Sisu
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, 2023-2024

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

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.

Teaching