Topology

• Main Author: Manetti, Marco
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
• Edition: 2nd ed. 2023.
• Series: La Matematica per il 3+2, 153.
• Subjects: Topology.; elektronické knihy; electronic books
• ISBN: 9783031321429; 9783031321412
• ISSN: 2038-5757 ;
• Physical Description: 1 online zdroj (383 stran).
• Access: Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty

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; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; 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. This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications. It also corrects some inaccuracies and some additional exercises are proposed. The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.