Topology

di Marco Manetti (Autore)

Springer, 2023

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.

• Autore: Marco Manetti
• Anno edizione: 2023
• Editore: Springer
• Formato: EPUB3 con Adobe DRM
• Lingua: Inglese
• Compatibilità: Tutti i dispositivi (eccetto Kindle)
• Layout: Reflowable
• EAN: 9783031321429