9780486469034 - topology for analysis (dover books on mathematics) von wilansky, albert (5 Ergebnisse)
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Zustand: New. pp. xiii + 383.
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Taschenbuch. Zustand: Neu. Neuware - Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
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Zustand: New. InhaltsverzeichnisrnrnIntroductionnTopological SpacenConvergencenSeparation AxiomsnTopological ConceptsnSup, Weak, Product, and Quotient TopologiesnCompactnessnCompactificationnComplete Semimetric SpacenMetrizationnUniformitynTopological Groupsn.
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Soft cover. Zustand: Fine. 1st Edition. [1st ed] ; xiii, 383 pages ; 24 cm. ; ISBN 9780486469034, 0486469034 ; OCLC 227923899 ; LCCN 2008026255 ; LC QA611 .W53 2008 ; Dewey 514 ; color pictorial stiff paper wrappers ; Originally published: Waltham, Mass. : Ginn, 1970 ; Contents: Introduction -- Explanatory Notes -- n-Space -- Ab…straction -- Topological Space -- Topological Space -- Semimetric and Metric Space -- Semimetric and Metric Topologies -- Natural Topologies and Metrics -- Notation and Terminology -- Base and Subbase -- Convergence -- Sequences -- Filters -- Partially Ordered Sets -- Nets -- Arithmetic of Nets -- Separation Axioms -- Separation by Open Sets -- Continuity -- Separation by Continuous Functions -- Topological Concepts -- Topological Properties -- Connectedness -- Separability -- Compactness -- Sup, Weak, Product, and Quotient Topologies -- Introduction -- Sup Topologies -- Weak Topologies -- Products -- Quotients -- Continuity -- Separation -- Compactness -- Countable and Sequential Compactness -- Compactness in Semimetric Space Ultrafilters Products -- Compactification -- The One-Point Compactification -- Embeddings -- The Stone-Cech Compactification -- Compactifications -- C- and C*-Embedding -- Realcompact Spaces -- Complete Semimetric Space -- Completeness -- Completion -- Baire Category -- Metrization -- Separable Spaces -- Local Finiteness -- Metrization -- Uniformity -- Uniform Space -- Uniform Continuity -- Uniform Concepts -- Uniformization Metrization and Completion -- Topological Groups -- Group Topologies -- Group Concepts -- Quotients -- Topological Vector Spaces -- Function Spaces -- The Compact Open Topology -- Topologies of Uniform Convergence -- Equicontinuity -- Weak Compactness -- Miscellaneous Topics -- Extremally Disconnected Spaces -- The Gleason Map -- Categorical Algebra -- Paracompact Spaces -- Ordinal Spaces -- The Tychonoff Plank -- Completely Regular and Normal Spaces AppendixTables of Theorems and Counterexamples -- Bibliography -- Index ; Appropriate for both students and professionals, this volume starts with the first principles of topology and advances to general analysis. Three levels of examples and problems, ordered and numbered by degree of difficulty, illustrate important concepts. A 40-page appendix, featuring tables of theorems and counter examples, provides a valuable reference. From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced. ; Albert "Tommy" Wilansky was a Canadian-American mathematician, known for introducing Smith numbers. From 1948 until his official retirement in 1992, Wilansky was a faculty member of the mathematics department of Lehigh University. He was the university's Distinguished Professor of Mathematics for the final 14 years of his tenure. During his 44 years at Lehigh he was a Fulbright visiting professor several times, at universities in Reading (1972-1973), London (1973), Tel Aviv (1981), and Berne (1981). Outside of academia he was a consultant for the Frankford Arsenal for the year 1957-1958. He was a professional musician for a brief time as a young man and continued playing piano and clarinet and writing songs, often with his wives and daughters. ; FINE. Book.
