Index analysis : approach theory at work / R. Lowen

• Autore: Lowen, Robert
• Pubblicazione: London, : Springer, 2015
• Titolo uniforme: Index analysis : approach theory at work
• Descrizione fisica: XXI, 466 p. : ill. ; 24 cm
• Soggetto topico: 06B35 - Continuous lattices and posets, applications [MSC 2020]; 06D22 - Frames, locales [MSC 2020]; 18F60 - Categories of topological spaces and continuous mappings [MSC 2020]; 46B04 - Isometric theory of Banach spaces [MSC 2020]; 54-XX - General topology [MSC 2020]; 54Exx - Topological spaces with richer structures [MSC 2020]; 60B10 - Convergence of probability measures [MSC 2020]; 68N30 - Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) [MSC 2020]
• Soggetto non controllato: Approach Space; Ascoli Theorem; Asymptotic Center; Asymptotic Radius; Completion; Contraction; Dini’s Theorem; Distance; Index; Limit Operator; Measure of Non-Compactness; Metric; Metric spaces; Opial’s Condition; Proximity; Topological spaces; Topology; Uniform Gauge Space; Uniform Spaces; Uniformity
• Nota di contenuto: The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis. Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories. Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.
• Titolo autorizzato: Index analysis : approach theory at work
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00113093
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: http://dx.doi.org/10.1007/978-1-4471-6485-2
• Serie: Springer monographs in mathematics Berlin [etc.] . -Springer , 1989-