Principles of Topology

by Fred H. Croom
Principles of Topology cover
Good Books rating 4.25
Education and Reference
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Waterstones
Paperback • £21.99
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  • ID: 7403
  • Added: 2025-12-14
  • Updated: 2025-12-30
  • ISBN: 9780486801544
  • Publisher: Courier Dover Publications
  • Published: 2016-02-17
  • Formats: 1
  • Reviews: 4

Principles of Topology is a comprehensive textbook that provides a solid foundation in the field of topology. Originally published in 1989, this slightly corrected edition offers a clear and rigorous introduction to the subject, making it accessible to both students and professionals. The book covers essential topics such as continuity, compactness, and connectedness, presenting them in a logical and coherent manner. It is designed to be a valuable resource for those seeking to understand the underlying principles of topology and its applications in various areas of mathematics. /n/n This textbook is known for its precise definitions, detailed explanations, and numerous examples that illustrate key concepts. It is suitable for advanced undergraduate and graduate students, as well as researchers in mathematics. The book's structured approach and thorough coverage make it an indispensable tool for anyone looking to deepen their understanding of topology.

Reviews
Reddit - r/math · 2017-01-01
excellent 4.50

The author is praised for clear writing and engaging examples. Historical context adds depth to the material.

This reviewer highlights Fred H. Croom's ability to make topology accessible and engaging. They appreciate the clear exposition and the inclusion of historical asides that provide context and motivation. The examples used are noted as particularly helpful in understanding the material. Overall, the book is seen as a well-written introduction to topology that balances rigor with accessibility.

Quick quotes

    Croom is an excellent author with well-written exposition

    motivating examples

    interesting historical asides to place the material in context

Mathematical Association of America · 2016-05-04
great 4.50

The book is a great introduction to point-set topology, suitable for diverse backgrounds. It is praised for its clarity and accessibility.

This review from the Mathematical Association of America commends the book as an excellent introduction to point-set topology. It is noted for its suitability for students with diverse backgrounds, making it a versatile text for various courses. The reviewer appreciates the clear and accessible presentation of the material, which makes complex concepts more approachable. The book's emphasis on geometric nature and practical applications is also highlighted as a strong point.

Quick quotes

    This is a very nice introduction to (mostly) point-set topology

    ideally suited for use as a text in courses where the students have diverse backgrounds

    written in a very clear lucid style

Goodreads · 2016-01-01
great 4.00

The book is rigorous yet not overly abstract, emphasizing the geometric nature of topology. It is praised for its clear and engaging style.

This reviewer appreciates the book's rigorous yet accessible approach to topology. They highlight the emphasis on the geometric nature of the subject and the applications of topological ideas to geometry and mathematics. The book is seen as a great resource for those looking to understand the fundamental principles of topology in a clear and engaging manner.

Quick quotes

    Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical ...

    This text presents the fundamental principles of topology rigorously but not abstractly.

    It is about the same level as Munkres' text but more down to earth

Goodreads · 2010-01-01
good 4.00

The text is rigorous yet not overly abstract, emphasizing the geometric aspects of topology. It is well-suited for undergraduate and graduate students.

This Goodreads review highlights the book's ability to present topology in a rigorous yet accessible manner. The emphasis on the geometric nature of the subject is particularly appreciated, making it easier for students to grasp abstract concepts. The reviewer notes that the book is suitable for both undergraduate and graduate students, as well as enthusiastic high schoolers. The clear and lucid style of writing is also praised, making the material more engaging and easier to understand.

Quick quotes

    This text presents the fundamental principles of topology rigorously but not abstractly

    It emphasizes the geometric nature of the subject

    written in a very clear lucid style

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