Elements of Abstract Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
2002
|
| Schriftenreihe: | Springer Undergraduate Mathematics Series
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In nature's infinite book of secrecy A little I can read. Antony and Cleopatra, 1. ii. This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role of mathematical logic, we present seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed- rings, linear spaces, metric spaces, and soon- and with many of the principal analytical concepts convergence, connectedness, continuity,compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of setbased mathematics and to consolidate an understanding of them in such a framework. To aid in these pursuits, we present our reader with things familiar and things new side by side in most parts of the book- and we sometimes adopt an unusual perspective. That this is not an analysis textbook is clear from its many omissions |
| Beschreibung: | 1 Online-Ressource (XII, 300 p) |
| ISBN: | 9781447101796 9781852334246 |
| ISSN: | 1615-2085 |
| DOI: | 10.1007/978-1-4471-0179-6 |
Internformat
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| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Searcóid, Mícheál Ó |
| author_facet | Searcóid, Mícheál Ó |
| author_role | aut |
| author_sort | Searcóid, Mícheál Ó |
| author_variant | m ó s mó mós |
| building | Verbundindex |
| bvnumber | BV042419345 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165486831 (DE-599)BVBBV042419345 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-0179-6 |
| format | Electronic eBook |
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| id | DE-604.BV042419345 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781447101796 9781852334246 |
| issn | 1615-2085 |
| language | English |
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| spelling | Searcóid, Mícheál Ó Verfasser aut Elements of Abstract Analysis by Mícheál Ó Searcóid London Springer London 2002 1 Online-Ressource (XII, 300 p) txt rdacontent c rdamedia cr rdacarrier Springer Undergraduate Mathematics Series 1615-2085 In nature's infinite book of secrecy A little I can read. Antony and Cleopatra, 1. ii. This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role of mathematical logic, we present seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed- rings, linear spaces, metric spaces, and soon- and with many of the principal analytical concepts convergence, connectedness, continuity,compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of setbased mathematics and to consolidate an understanding of them in such a framework. To aid in these pursuits, we present our reader with things familiar and things new side by side in most parts of the book- and we sometimes adopt an unusual perspective. That this is not an analysis textbook is clear from its many omissions Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s 1\p DE-604 Funktionalanalysis (DE-588)4018916-8 s 2\p DE-604 https://doi.org/10.1007/978-1-4471-0179-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Searcóid, Mícheál Ó Elements of Abstract Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4001865-9 |
| title | Elements of Abstract Analysis |
| title_auth | Elements of Abstract Analysis |
| title_exact_search | Elements of Abstract Analysis |
| title_full | Elements of Abstract Analysis by Mícheál Ó Searcóid |
| title_fullStr | Elements of Abstract Analysis by Mícheál Ó Searcóid |
| title_full_unstemmed | Elements of Abstract Analysis by Mícheál Ó Searcóid |
| title_short | Elements of Abstract Analysis |
| title_sort | elements of abstract analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis |
| url | https://doi.org/10.1007/978-1-4471-0179-6 |
| work_keys_str_mv | AT searcoidmichealo elementsofabstractanalysis |