Unit information: Metric Spaces in 2019/20

Unit name	Metric Spaces
Unit code	MATH20006
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. Viveka Erlandsson
Open unit status	Not open
Pre-requisites	MATH10011 Analysis and MATH10010 Introduction to Proofs and Group Theory
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

To introduce metric and topological spaces and to extend some theorems about convergence and continuity in the case of sequences of real numbers and real-valued functions of one real variable.

Unit Description

This course generalizes some theorems about convergence and continuity of functions from the Level 4 unit Analysis 1, and develops a theory of convergence and uniform convergence in any metric space. Topics will include basic topology (open, closed, compact, connected sets), continuity of functions, completeness, the contraction mapping theorem and applications, compactness and connectedness.

Relation to Other Units

This unit is a member of a sequence of analysis units at levels 5, 6 and 7. It is a prerequisite for Measure Theory and Integration, Advanced Topics in Analysis, and Functional Analysis.

Intended Learning Outcomes

At the end of the course the student should know and understand the definitions and theorems (and their proofs) and should be able to use the ideas of the course in unseen situations.

Teaching Information

Lectures and problem classes.

Assessment Information

• 90% Exam
• 10% Coursework (2 x 5%)

Reading and References

Recommended

• J.C. Burkill and H. Burkill, A Second Course in Mathematical Analysis, Cambridge University Press, 2002
• Irving Kaplansky, Set Theory and Metric Spaces, Chelsea Publishing Company, 1977
• Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976
• W. A. Sutherland, Introduction to Metric and Topological Spaces, Clarendon Press, 2009