Beyond topology / / Frédéric Mynard, Elliott Pearl, editors

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2009]; ©2009
• Descrizione fisica: 1 online resource (395 p.)
• Disciplina: 514
• Soggetto topico: Topological spaces; Topology
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): MynardFrédéric <1973->; PearlElliott
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""Preface""; ""Categorical Topology""; ""1. Introduction""; ""2. Topological constructs""; ""3. Limits and topological constructs""; ""4. Special morphisms""; ""5. Fiber-small topological constructs""; ""6. Reflective and coreflective subcategories""; ""7. Convenience properties""; ""8. Convenient hulls""; ""9. Topological hull = MacNeille completion""; ""References""; ""A Convenient Setting for Completions and Function Spaces""; ""1. Introduction: Why go beyond Top""; ""2. The category of merotopic spaces and some of its subcategories""; ""3. Smallness and nearness"" ; ""4. Filter spaces and limit spaces""""5. Separation and regularity for nearness spaces""; ""6. Completion theory for nearness spaces""; ""7. Separation and regularity for Cauchy spaces""; ""8. Completion theory for Cauchy spaces""; ""9. A comparison of the completion theories for subtopological spaces""; ""10. Function spaces""; ""11. Relations to other constructs""; ""12. Where to find more information""; ""References""; ""Proximity: a powerful tool in extension theory, function spaces, hyperspaces, boolean algebras and point-free geometry""; ""1. Introduction""; ""2. Axiomatisations"" ; ""3. Topology associated with a given proximity space""""4. Interplay between proximity and uniformity""; ""5. Compactifications and proximities: Smirnov theorem""; ""6. Leader's contribution""; ""7. Proximity in complex frameworks""; ""8. Lattice theoretical approach and point-free geometry""; ""References""; ""An Initiation into Convergence Theory""; ""1. Introduction""; ""2. Filters""; ""2.1. Neighborhood filters""; ""2.2. Principal filters""; ""2.3. Cofinite filters""; ""2.4. Sequential filters""; ""2.5. Countably based filters""; ""2.6. Grills""; ""2.7. Order, ultrafilters"" ; ""2.8. Decomposition""""2.9. Stone transform""; ""3. Basic classes of convergences""; ""3.1. Topologies""; ""3.2. Sequentially based convergences""; ""3.3. Convergences of countable character""; ""3.4. Pretopologies""; ""4. Continuity""; ""4.1. Initial convergences""; ""4.2. Final convergences""; ""4.3. Continuity in subclasses""; ""4.4. Products""; ""4.5. Powers""; ""5. Adherences""; ""6. Covers""; ""7. Compactness""; ""7.1. Compact families""; ""7.2. Weaker versions of compactness""; ""7.3. Countable compactness""; ""7.4. Finite compactness""; ""7.5. Sequential compactness"" ; ""8. Adherence-determined convergences""""8.1. Pseudotopologies""; ""8.2. Narrower classes of adherence-determined convergences""; ""9. Diagonality and regularity""; ""9.1. Contours""; ""9.2. Hausdorff convergences""; ""9.3. Diagonality""; ""9.4. Regularity""; ""9.5. Interactions between regularity and topologicity""; ""10. Filter-determined convergences""; ""11. Categories of convergence spaces""; ""11.1. Abstract and concrete categories""; ""11.2. Subcategories of convergence spaces""; ""12. Functorial inequalities""; ""13. Quotient maps""; ""14. Power convergences"" ; ""14.1. Topologicity and other properties of power convergences""
• Titolo autorizzato: Beyond topology
• ISBN: 0-8218-8165-5; 0-8218-4279-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480270903321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society) ; ; v. 486.