An illustrated introduction to topology and homotopy. (2014)

• Record Type: Book
• Further Information: Note: Sasho Kalajdzievski.
• Authors: Kalajdzievski, Sasho
• Contents: TOPOLOGY; Sets, Numbers, Cardinals, and Ordinals; Sets and Numbers; Sets and Cardinal Numbers; Axiom of Choice and Equivalent Statements Metric Spaces: Definition, Examples, and Basics; Metric Spaces: Definition and Examples; Metric Spaces: Basics Topological Spaces: Definition and Examples; The Definition and Some Simple Examples; Some Basic Notions; Bases; Dense and Nowhere Dense Sets; Continuous Mappings Subspaces, Quotient Spaces, Manifolds, and CW-Complexes; Subspaces; Quotient Spaces; The Gluing Lemma, Topological Sums, and Some Special Quotient Spaces; Manifolds and CW-Complexes Products of Spaces; Finite Products of Spaces; Infinite Products of Spaces; Box Topology Connected Spaces and Path Connected Spaces; Connected Spaces: Definition and Basic Facts; Properties of Connected Spaces; Path Connected Spaces; Path Connected Spaces: More Properties and Related Matters; Locally Connected and Locally Path Connected Spaces Compactness and Related Matters; Compact Spaces: Definition; Properties of Compact Spaces; Compact, Lindelöf, and Countably Compact Spaces; Bolzano, Weierstrass, and Lebesgue; Compactification; Infinite Products of Spaces and Tychonoff Theorem Separation Properties; The Hierarchy of Separation Properties; Regular Spaces and Normal Spaces; Normal Spaces and Subspaces Urysohn, Tietze, and Stone-Čech; Urysohn Lemma; The Tietze Extension Theorem; Stone-Čech Compactification HOMOTOPY; Isotopy and Homotopy; Isotopy and Ambient Isotopy; Homotopy; Homotopy and Paths; The Fundamental Group of a Space The Fundamental Group of a Circle and Applications; The Fundamental Group of a Circle; Brouwer Fixed Point Theorem and the Fundamental Theorem of Algebra; The Jordan Curve Theorem Combinatorial Group Theory ; Group Presentations; Free Groups, Tietze, Dehn; Free Products and Free Products with Amalgamation Seifert–van Kampen Theorem and Applications ; Seifert–van Kampen Theorem; Seifert–van Kampen Theorem: Examples; The Seifert–van Kampen Theorem and Knots; Torus Knots and Alexander’s Horned Sphere; Links On Classifying Manifolds and Related Topics; 1-Manifolds; Compact 2-Manifolds: Preliminary Results; Compact 2-Manifolds: Classification; Regarding Classification of CW-Complexes and Higher Dimensional Manifolds; Higher Homotopy Groups: A Brief Overview Covering Spaces, Part 1; Covering Spaces: Definition, Examples, and Preliminaries; Lifts of Paths; Lifts of Mappings; Covering Spaces and Homotopy Covering Spaces, Part 2; Covering Spaces and Sheets; Covering Trans formations; Covering Spaces and Groups Acting Properly Discontinuously; Covering Spaces: Existence; The Borsuk–Ulam Theorem Applications in Group Theory ; Cayley Graphs and Covering Spaces; Topographs and Presentations; Subgroups of Free Groups; Two Subgroup Theorems Bibliography
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource, illustrations
• Subjects: 514; Topology; Homotopy theory
• Languages: English
• ISBNs: 9781482220827; 9781482220810
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.