Elements of Abstract Analysis

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9781852334246: Elements of Abstract Analysis
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While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Recensione:

From the reviews of the first edition:

BULLETIN OF MATHEMATICS BOOKS

"...an interesting mix of algebra, topology and functional analysis, with chapter titles like Algebraic Structure, Linear Structure, Geometric Structure and Topological Structure."

"Michael O’Searcoid’s book ‘Element of Abstract Analysis’ is a book that deals with the fundamental principles of mathematics in a broad framework of set-theoretic approach. The book is written with a deep insight. ... The contents are conceptually useful to students. ... The book is a nice readable treat for every student of mathematics and is highly recommended for one semester course at M.Sc. level." (Madhu Tiwari, Journal of the Indian Academy of Mathematics, Vol. 25 (1), 2003)

"This book covers the elements of abstract analysis, treated mostly within the context of topological spaces. ... This is a carefully written book, starting from set-theoretic axioms, and containing about 180 problems and exercises with hints and solutions. It is an ideal source of information for independent student study. There is a comprehensive index." (European Mathematical Society Newsletter, September, 2002)

"The book presents some concepts of analysis and the mathematical structures which enfold them. ... the reviewer recommends the book to everyone interested in analysis, especially those scholars interested in studying more advanced areas like Functional Analysis, or Operator Theory." (Catalin Badea, Zentralblatt MATH, Vol. 999 (24), 2002)

"The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed ... . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. This book is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

"This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. ... The book is written specifically for final-year and undergraduate students who should already be familiar with most of the mathematical structures discussed ... and with many of the principal analytical concepts ... . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics." (Zentralblatt für Didaktik der Mathematik, February, 2002)

Contenuti:

1. Sets.- 1.1 Set Theory.- 1.2 Relations and Functions.- 1.3 Ordered Sets.- 1.4 Ordinals.- 1.5 The Axiom of Choice.- 2. Counting.- 2.1 Counting Numbers.- 2.2 Cardinality.- 2.3 Enumeration.- 2.4 Cardinality of Unions and Products.- 3. Algebraic Structure.- 3.1 Elementary Algebraic Structures.- 3.2 Vector Spaces.- 3.3 Algebras.- 3.4 Preservation of Algebraic Structure.- 4. Analytic Structure.- 4.1 Ordered Algebraic Structure.- 4.2 Number Systems.- 4.3 Real and Complex Functions.- 4.4 Inequalities.- 5. Linear Structure.- 5.1 Linear Spaces and Algebras.- 5.2 Linear Shapes.- 5.3 Linear Functionals.- 6. Geometric Structure.- 6.1 Semimetrics and Metrics.- 6.2 Seminorms and Norms.- 6.3 Sesquilinear Forms and Inner Products.- 7. Topological Structure.- 7.1 Topologies.- 7.2 Neighbourhoods.- 7.3 Cardinality and Topology.- 7.4 Separation.- 8. Continuity and Openness.- 8.1 Preservation of Topological Structure.- 8.2 Topologies Denned by Functions.- 8.3 Derived Topological Spaces.- 8.4 Topologies on Linear Spaces.- 9. Connectedness.- 9.1 Connected Spaces.- 9.2 Pathwise Connectedness.- 10. Convergence.- 10.1 Filters.- 10.2 Limits.- 11. Compactness.- 11.1 Compact Topological Spaces.- 11.2 Compact Hausdorff Spaces.- 11.3 Local Compactness.- 12. Completeness.- 12.1 Complete Metric Spaces.- 12.2 Banach Spaces.- 12.3 Hilbert Spaces.- 12.4 Banach Algebras.- Solutions.

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Mícheál Ó Searcóid
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Descrizione libro Springer London Ltd, United Kingdom, 2001. Paperback. Condizione: New. 2002 ed.. Language: English . Brand New Book ***** Print on Demand *****.While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis. Codice articolo AAV9781852334246

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Descrizione libro Springer, 2016. Paperback. Condizione: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice articolo ria9781852334246_lsuk

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Descrizione libro Springer London Ltd, 2001. PAP. Condizione: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice articolo IQ-9781852334246

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Descrizione libro Springer London Ltd, United Kingdom, 2001. Paperback. Condizione: New. 2002 ed.. Language: English . Brand New Book ***** Print on Demand *****. While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis. Codice articolo AAV9781852334246

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Descrizione libro Springer London Ltd, United Kingdom, 2001. Paperback. Condizione: New. 2002 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis. Codice articolo LIE9781852334246

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Descrizione libro Springer, 2001. Paperback. Condizione: NEW. 9781852334246 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Codice articolo HTANDREE0415932

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Descrizione libro Springer London Ltd, 2001. PAP. Condizione: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice articolo LQ-9781852334246

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Descrizione libro Springer, 2018. Paperback. Condizione: New. Never used! This item is printed on demand. Codice articolo 185233424X

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Descrizione libro Springer 11/9/2001, 2001. Paperback or Softback. Condizione: New. Elements of Abstract Analysis. Book. Codice articolo BBS-9781852334246

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