Foundations of Real and Abstract Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Graduate Texts in Mathematics
174 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The core of this book, Chapters 3 through 5, presents a course on metric, normed,andHilbertspacesatthesenior/graduatelevel. Themotivationfor each of these chapters is the generalisation of a particular attribute of the n Euclidean spaceR : in Chapter 3, that attribute isdistance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem(3. 3. 12)showingthattheLebesguecoveringpropertyisequivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts oftheirmathematicalstudies,studentscontrivetoavoidanalysiscoursesat almost any cost, in particular that of their own educational and technical deprivation. Many universities have at times capitulated to the negative demand of students for analysis courses and have seriously watered down their expectations of students in that area. As a result, mathematics - jors are graduating, sometimes with high honours, with little exposure to anything but a rudimentary course or two on real and complex analysis, often without even an introduction to the Lebesgue integral |
| Beschreibung: | 1 Online-Ressource (XIV, 322 p) |
| ISBN: | 9780387226200 9780387982397 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/b97625 |
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| 500 | |a The core of this book, Chapters 3 through 5, presents a course on metric, normed,andHilbertspacesatthesenior/graduatelevel. Themotivationfor each of these chapters is the generalisation of a particular attribute of the n Euclidean spaceR : in Chapter 3, that attribute isdistance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem(3. 3. 12)showingthattheLebesguecoveringpropertyisequivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts oftheirmathematicalstudies,studentscontrivetoavoidanalysiscoursesat almost any cost, in particular that of their own educational and technical deprivation. Many universities have at times capitulated to the negative demand of students for analysis courses and have seriously watered down their expectations of students in that area. As a result, mathematics - jors are graduating, sometimes with high honours, with little exposure to anything but a rudimentary course or two on real and complex analysis, often without even an introduction to the Lebesgue integral | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/b97625 |
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| institution | BVB |
| isbn | 9780387226200 9780387982397 |
| issn | 0072-5285 |
| language | English |
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| spelling | Bridges, Douglas S. Verfasser aut Foundations of Real and Abstract Analysis by Douglas S. Bridges New York, NY Springer New York 1998 1 Online-Ressource (XIV, 322 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 174 0072-5285 The core of this book, Chapters 3 through 5, presents a course on metric, normed,andHilbertspacesatthesenior/graduatelevel. Themotivationfor each of these chapters is the generalisation of a particular attribute of the n Euclidean spaceR : in Chapter 3, that attribute isdistance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem(3. 3. 12)showingthattheLebesguecoveringpropertyisequivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts oftheirmathematicalstudies,studentscontrivetoavoidanalysiscoursesat almost any cost, in particular that of their own educational and technical deprivation. Many universities have at times capitulated to the negative demand of students for analysis courses and have seriously watered down their expectations of students in that area. As a result, mathematics - jors are graduating, sometimes with high honours, with little exposure to anything but a rudimentary course or two on real and complex analysis, often without even an introduction to the Lebesgue integral Mathematics Real Functions Operations Research/Decision Theory Mathematik Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s 1\p DE-604 https://doi.org/10.1007/b97625 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bridges, Douglas S. Foundations of Real and Abstract Analysis Mathematics Real Functions Operations Research/Decision Theory Mathematik Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Foundations of Real and Abstract Analysis |
| title_auth | Foundations of Real and Abstract Analysis |
| title_exact_search | Foundations of Real and Abstract Analysis |
| title_full | Foundations of Real and Abstract Analysis by Douglas S. Bridges |
| title_fullStr | Foundations of Real and Abstract Analysis by Douglas S. Bridges |
| title_full_unstemmed | Foundations of Real and Abstract Analysis by Douglas S. Bridges |
| title_short | Foundations of Real and Abstract Analysis |
| title_sort | foundations of real and abstract analysis |
| topic | Mathematics Real Functions Operations Research/Decision Theory Mathematik Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematics Real Functions Operations Research/Decision Theory Mathematik Analysis |
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