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Topology

  • Marco Manetti

Part of the UNITEXT book series (UNITEXT, volume 91)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 91)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marco Manetti
    Pages 1-19
  3. Marco Manetti
    Pages 21-38
  4. Marco Manetti
    Pages 39-62
  5. Marco Manetti
    Pages 63-85
  6. Marco Manetti
    Pages 87-104
  7. Marco Manetti
    Pages 105-128
  8. Marco Manetti
    Pages 161-164
  9. Marco Manetti
    Pages 165-180
  10. Marco Manetti
    Pages 181-198
  11. Marco Manetti
    Pages 199-217
  12. Marco Manetti
    Pages 219-238
  13. Marco Manetti
    Pages 239-260
  14. Marco Manetti
    Pages 279-303
  15. Back Matter
    Pages 305-309

About this book

Introduction

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises.

The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Keywords

Compact spaces Covering space Fundamental group Topological spaces van Kampen theorem

Authors and affiliations

  • Marco Manetti
    • 1
  1. 1.Department of MathematicsSapienza - Università di RomaRomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16958-3
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16957-6
  • Online ISBN 978-3-319-16958-3
  • Series Print ISSN 2038-5714
  • Buy this book on publisher's site