About this book
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.
- 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
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