Point-Set Topology : A Working Textbook

• Record Nr.: UNINA9910865252603321
• Autore: López Rafael
• Pubbl/distr/stampa: Cham : , : Springer International Publishing AG, , 2024; ©2024
• ISBN: 9783031585135; 9783031585128
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (397 pages)
• Collana: Springer Undergraduate Mathematics Series
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 2 Topological Spaces -- 2.1 Topological Spaces and Examples -- 2.2 Basis for a Topology -- 2.3 The Euclidean Topology -- 2.4 Subbasis for a Topology -- 2.5 Topological Subspaces -- 2.6 Worked Exercises -- 2.7 Suggested Exercises -- 3 Proximity on a Topological Space -- 3.1 Neighborhoods of a Point -- 3.2 Basis of Neighborhoods -- 3.3 Interior and Closure -- 3.4 Convergence of Sequences -- 3.5 Worked Exercises -- 3.6 Suggested Exercises -- 4 Metric Spaces -- 4.1 Distance and Metric Spaces -- 4.2 Topology on a Metric Space -- 4.3 Interior and Closure in a Metric Space -- 4.4 Convergence of Sequences in a Metric Space -- 4.5 Worked Exercises -- 4.6 Suggested Exercises -- 5 Continuity -- 5.1 Continuous Mappings -- 5.2 Properties of Continuous Maps -- 5.3 Continuous Maps on Euclidean Spaces -- 5.4 Worked Exercises -- 5.5 Suggested Exercises -- 6 Homeomorphisms and Topological Invariants -- 6.1 Homeomorphisms -- 6.2 Topological Invariants -- 6.3 Construction of Homeomorphisms in Euclidean Spaces -- 6.4 Embeddings and Open Maps -- 6.5 Worked Exercises -- 6.6 Suggested Exercises -- 7 Product Topology -- 7.1 The Product Topology -- 7.2 Product Topology and Continuity -- 7.3 Product Topology: The Infinite Case -- 7.4 Worked Exercises -- 7.5 Suggested Exercises -- 8 Connectedness -- 8.1 Connected Spaces and Examples -- 8.2 Further Properties of Connectedness -- 8.3 Connected Components -- 8.4 ; Path Connectedness -- 8.5 Worked Exercises -- 8.6 Suggested Exercises -- 9 Compactness -- 9.1 Compact Spaces and Examples -- 9.2 Compactness in Euclidean Spaces -- 9.3 Worked Exercises -- 9.4 Suggested Exercises -- 10 Quotient Topology -- 10.1 Motivation and Definition of the Quotient Topology -- 10.2 Final Topology and Identifications -- 10.3 Construction of Homeomorphisms in a Quotient Space.; 10.4 Maps Between Quotient Spaces -- 10.5 Worked Exercises -- 10.6 Suggested Exercises -- 11 The Fundamental Group -- 11.1 Homotopy and Loops -- 11.2 The Fundamental Group of S1 -- 11.3 The Fundamental Group of Sn, n≥2 -- 11.4 Retractions -- 11.5 Worked Exercises -- 11.6 Suggested Exercises -- Bibliography -- Index.