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.
| Autor: | Manetti, Marco |
|---|---|
| ISBN: | 9783319169576 |
| Sprache: | Englisch |
| Seitenzahl: | 309 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer International Publishing |
| Veröffentlicht: | 10.06.2015 |
| Schlagworte: | Compact spaces Covering space Fundamental group Topological spaces van Kampen theorem |
Prof. Marco Manetti , Dipartimento di Matematica "Guido Castelnuovo", Sapienza - Università di Roma, Roma, Italy.