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 |
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.
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.
Lectures and problem classes.
Recommended