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Metric Spaces
The abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract c...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Springer London : Imprint: Springer,
2007.
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| Edición: | 1st ed. 2007. |
| Colección: | Springer Undergraduate Mathematics Series,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 005 | 20220116142051.0 | ||
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| 020 | |a 9781846286278 |9 978-1-84628-627-8 | ||
| 024 | 7 | |a 10.1007/978-1-84628-627-8 |2 doi | |
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| 100 | 1 | |a O'Searcoid, Mícheál. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Metric Spaces |h [electronic resource] / |c by Mícheál O'Searcoid. |
| 250 | |a 1st ed. 2007. | ||
| 264 | 1 | |a London : |b Springer London : |b Imprint: Springer, |c 2007. | |
| 300 | |a XX, 304 p. 102 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
| 505 | 0 | |a Metrics -- Distance -- Boundary -- Open, Closed and Dense Subsets -- Balls -- Convergence -- Bounds -- Continuity -- Uniform Continuity -- Completeness -- Connectedness -- Compactness -- Equivalence. | |
| 520 | |a The abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease. The book goes on to provide a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length. Other features include: end-of-chapter summaries and numerous exercises to reinforce what has been learnt; extensive cross-referencing to help the reader follow arguments; a Cumulative Reference Chart, showing the dependencies throughout the book on a section-by-section basis as an aid to course design. The book is designed for third- and fourth-year undergraduates and beginning graduates. Readers should have some practical knowledge of differential and integral calculus and have completed a first course in real analysis. With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Topology. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Topology. |
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| 776 | 0 | 8 | |i Printed edition: |z 9781848004948 |
| 776 | 0 | 8 | |i Printed edition: |z 9781846283697 |
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| 830 | 0 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
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