# TIES676 COM2: Baire's theorem and some of its consequences (2–3 cr)

**Study level:**

Advanced studies

**Grading scale:**

Pass - fail

**Language:**

English

**Responsible organisation:**

Faculty of Information Technology

**Curriculum periods:**

2017-2018, 2018-2019, 2019-2020

## Description

##### Content

In this course, we discuss Baire's category theorem, that is, roughly speaking, a complete metric space is thick in a certain sense. We provide corollaries thereof, such as the closed graph theorem or the open mapping theorem. We will further prove that the algebraic dimension of an infinite dimensional Banach space is necessarily uncountable. The results have also implications for numerical analysis.

## Learning outcomes

Baire's category theorem

## Description of prerequisites

Basic knowledge of Banach spaces

## Completion methods

### Method 1

Select all marked parts

**Parts of the completion methods**

x

### Teaching (2–3 cr)

**Type:**

Participation in teaching

**Grading scale:**

Pass - fail

**Language:**

English