Undergraduate topology : a working textbook / Aisling McCluskey, Brian McMaster.

Format:

Book

Author/Creator:

McCluskey, Aisling, author.

McMaster, Brian, author.

Language:

English

Subjects (All):

Mathematics.

Physical Description:

1 online resource (157 p.)

Edition:

First edition.

Place of Publication:

New York, New York : Oxford University Press, 2014.

Language Note:

English

Summary:

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i

Contents:

Cover; Preface; Contents; Comments to the instructor: what types of study this book will support; Comments to the student reader: how to use this book; 1 Introduction; Preamble; Sets and mappings; Zorn's lemma; The least uncountable ordinal; Metric spaces; Expansion of Chapter 1; 2 Topological spaces; Some elementary concepts; Subspaces; Expansion of Chapter 2; 3 Continuity and convergence; Continuity; Convergent sequences; Nets; Filters; Expansion of Chapter 3; 4 Invariants; Sequential compactness; Compactness; Local compactness; Connectedness; Separability; Expansion of Chapter 4

5 Base and productBase; Complete separability; Product spaces; Product theorems; Infinite products; Expansion of Chapter 5; 6 Separation axioms; T1 spaces; T2 spaces; T3 spaces; T3 1/2 spaces; T4 spaces; Expansion of Chapter 6; Essential Exercises; Solutions to selected exercises; Suggestions for further reading; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-100673-4

0-19-100672-6

OCLC:

884547851