Theorems and Problems in Functional Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1982
|
| Schriftenreihe: | Problem Books in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Even the simplest mathematical abstraction of the phenomena of reality the real line- can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathematical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures |
| Beschreibung: | 1 Online-Ressource (IX, 347 p) |
| ISBN: | 9781461381532 9781461381556 |
| ISSN: | 0941-3502 |
| DOI: | 10.1007/978-1-4613-8153-2 |
Internformat
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-8153-2 |
| format | Electronic eBook |
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| isbn | 9781461381532 9781461381556 |
| issn | 0941-3502 |
| language | English |
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| spelling | Kirillov, A. A. Verfasser aut Theorems and Problems in Functional Analysis by A. A. Kirillov, A. A. Gvishiani New York, NY Springer US 1982 1 Online-Ressource (IX, 347 p) txt rdacontent c rdamedia cr rdacarrier Problem Books in Mathematics 0941-3502 Even the simplest mathematical abstraction of the phenomena of reality the real line- can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathematical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Funktionalanalysis (DE-588)4018916-8 s 2\p DE-604 Gvishiani, A. A. Sonstige oth https://doi.org/10.1007/978-1-4613-8153-2 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 | Kirillov, A. A. Theorems and Problems in Functional Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4143389-0 |
| title | Theorems and Problems in Functional Analysis |
| title_auth | Theorems and Problems in Functional Analysis |
| title_exact_search | Theorems and Problems in Functional Analysis |
| title_full | Theorems and Problems in Functional Analysis by A. A. Kirillov, A. A. Gvishiani |
| title_fullStr | Theorems and Problems in Functional Analysis by A. A. Kirillov, A. A. Gvishiani |
| title_full_unstemmed | Theorems and Problems in Functional Analysis by A. A. Kirillov, A. A. Gvishiani |
| title_short | Theorems and Problems in Functional Analysis |
| title_sort | theorems and problems in functional analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionalanalysis Aufgabensammlung |
| url | https://doi.org/10.1007/978-1-4613-8153-2 |
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