# MATS213 Metric Spaces (5 cr)

Study level:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Metric spaces, continuity and limits, completeness, compactness and connectedness

## Learning outcomes

After passing the course the student:

• knows and understands the definitions of a metric, a metric space, and open and closed sets
• knows how handle sequences and functions in metric spaces
• knows what the completeness of a metric space means
• knows and understands the definitions of compact and connected sets in abstract metric spaces
• can apply the methods and proofs of the course to different problems
• has improved his/her abilities to understand course related concepts in applications

## Description of prerequisites

Introduction to mathematical analysis 2, vector analysis 1

## Study materials

Applicable parts of J. Väisälä: Topology 1

M. Bruckner, J. B. Bruckner, and B. S. Thomson: Real analysis. 2nd edition, 2008. chapter 9.

## Literature

• M. Bruckner, J. B. Bruckner, and B. S. Thomson: Real analysis. 2nd edition, 2008.
• John B. Conway: A first course in analysis

## Completion methods

### Method 1

Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 1
Select all marked parts

### Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Language:
Finnish
Study methods:

Lectures and homework. Course exam.

Study materials:

Soveltuvin osin J. Väisälä: Topologia I

x

Type:
Exam