# 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

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.