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  • Point-Set Topology: A Working Textbook (Springer Undergraduate Mathematics Series)

Point-Set Topology: A Working Textbook (Springer Undergraduate Mathematics Series)

by Rafael López (Author) Format: Paperback
5.0 out of 5 stars (3)
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This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular.

Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group.

Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.

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  1. ISBN-10
    3031585127
  2. ISBN-13
    978-3031585128
  3. Edition
    2024th
  4. Publisher
    Springer
  5. Publication date
    June 2, 2024
  6. Language
    English
  7. Dimensions
    1.3 x 0.5 x 8.6 inches
  8. Print length
    406 pages
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Editorial Reviews

Review

“This book is intended as a companion book to intermediate or introductory texts on general topology, so it contains theorems … illustrated by many working examples (more than 160), worked exercises with full solutions (almost 300) and suggested exercises without solutions. … I hope that this valuable workbook, meeting all the requirements of demanding modern pedagogy will be widely used as companion to various textbooks and will contribute to raise the level of teaching the contemporary general topology for undergraduates.” (Włodzimierz Ślęzak, zbMATH 1554.54001, 2025)

From the Back Cover

This textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular.

Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group.

Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.

Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ June 2, 2024
  • Edition ‏ : ‎ 2024th
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 406 pages
  • ISBN-10 ‏ : ‎ 3031585127
  • ISBN-13 ‏ : ‎ 978-3031585128
  • Item Weight ‏ : ‎ 1.5 pounds
  • Dimensions ‏ : ‎ 1.3 x 0.5 x 8.6 inches
  • Best Sellers Rank: #2,543,085 in Books (See Top 100 in Books)
  • Customer Reviews:
    5.0 out of 5 stars (3)

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Customer reviews

5 out of 5 stars
3 global ratings

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Top reviews from other countries

  • Hendrik Lorentz
    5 out of 5 stars
    Exactly what I was looking for!
    Reviewed in Germany on August 10, 2024
    Format: Paperback
    Brief content visible, double tap to read full content.
    Full content visible, double tap to read brief content.

    Book has a great printing quality: smooth/glossy paper, sharp text, and no ghosting. Occasionally contains colorful figures (where applicable - this is a topology book after all)

    I am a data scientist teaching myself higher mathematics in my free time with the hope that one day I’ll move on from building mundane classification models in tech companies to doing proper machine learning research.

    This is precisely the kind of book that suits my needs: I have no access to lecturers, or to anyone else who is a mathematician. Being able to validate my solutions and check whether I have indeed understood concepts is absolutely crucial for me.

    Exactly what I was looking for!
    Exactly what I was looking for!
    Exactly what I was looking for!
    Exactly what I was looking for!
    Hendrik Lorentz
    5 out of 5 stars
    Exactly what I was looking for!
    Reviewed in Germany on August 10, 2024
    Format: Paperback

    Book has a great printing quality: smooth/glossy paper, sharp text, and no ghosting. Occasionally contains colorful figures (where applicable - this is a topology book after all)

    I am a data scientist teaching myself higher mathematics in my free time with the hope that one day I’ll move on from building mundane classification models in tech companies to doing proper machine learning research.

    This is precisely the kind of book that suits my needs: I have no access to lecturers, or to anyone else who is a mathematician. Being able to validate my solutions and check whether I have indeed understood concepts is absolutely crucial for me.

    Sending feedback...
    Thanks, we'll investigate in the next few days.
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