MA222 - Metric Spaces

Table of contents

• Content & Summaries
• Reading List

Multi

Module Info

Module Link/Module Webpage/Lecture Notes

Professor: Andras Mathe
Term: 2
Status: Core
Assessment: 85% exam, 15% Assignments

• Past Papers

Assumed Knowledge:

• MA142—Calculus 1 Sequences, convergence, Cauchy sequences, series, continuous functions, differentiable functions
• MA138—Sets and Numbers Set theory, proofs, cardinality
• MA271—Mathematical Analysis 3 Pointwise and uniform convergence of sequences of functions, Open and closed sets in Rn

Rating

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Content & Summaries

Introduction

Topic	Rating	Summary
Normed, Metric and Topological spaces
Open and closed sets and their relation to continuity
Notions of Compactness and relations to continuous maps
Notions of Completeness and relations to previous topics in the module

Reading List

• W A Sutherland, Introduction to Metric and Topological Spaces, oup.
• E T Copson, Metric Spaces, cup.
• W Rudin, Principles of Mathematical Analysis, McGraw Hill.
• G W Simmons, Introduction to Topology and Modern Analysis, McGraw Hill.
• A M Gleason, Fundamentals of Abstract Analysis, Jones and Bartlett.