SØG - mellem flere end 8 millioner bøger:
Viser: Introduction to Metric and Topological Spaces
Introduction to Metric and Topological Spaces
Wilson A. Sutherland
(2009)
Sprog: Engelsk
Oxford University Press, Incorporated
593,00 kr.
ikke på lager, Bestil nu og få den leveret
om ca. 15 hverdage
om ca. 15 hverdage
Detaljer om varen
- 2. Udgave
- Undefined: 224 sider
- Udgiver: Oxford University Press, Incorporated (Oktober 2009)
- ISBN: 9780199563081
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics.
Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments.
The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments.
The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Preface1. Introduction2. Notation and terminology3. More on sets and functions4. Review of some real analysis5. Metric spaces6. More concepts in metric spaces7. Topological spaces8. Continuity in topological spaces; bases9. Some concepts in topological spaces10. Subspaces and product spaces11. The Hausdorff condition12. Connected spaces13. Compact spaces14. Sequential compactness15. Quotient spaces and surfaces16. Uniform convergence17. Complete metric spacesReferencesIndex
De oplyste priser er inkl. moms
Butikker og åbningstid
Handler du som firma
Forretningsbetingelser
Porto og forsendelse
Data & cookiepolitik
Handler du som firma
Forretningsbetingelser
Porto og forsendelse
Data & cookiepolitik
Find pensumliste
FAQ for studerende
Pensumlistegaranti
Sortiment og levering
Kompendier(for undervisere)
FAQ for studerende
Pensumlistegaranti
Sortiment og levering
Kompendier(for undervisere)
Polyteknisk Boghandel og Forlag A/S - Anker Engelundsvej 1 - 2800 Lyngby
Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927
Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927