Allgemeine Topologie Book by G. Preuss - Bookswagon
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Allgemeine Topologie

Allgemeine Topologie


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About the Book

Die allgemeine Topologie, gelegentlich auch analytische oder mengentheoretische Topologie genannt, ist entstanden aus dem Bestreben, die aus der Analysis bekannten Begriffe wie Stetigkeit und Konvergenz auf eine allgemeine Grund- lage zu stellen. Es soll hier nicht versucht werden, die historische Entwicklung aufzuzeigen, sondern viel- mehr soll das Ergebnis jahrzehntelanger Forschungsarbeit in Form einer axiomatisch aufgebauten Theorie prasentiert werden. Dabei werden auch neueste Forschungsergebnisse berUcksichtigt. Langst hat sich die allgemeine Topologie 10sgelBst von der Analysis und zu einer selbstandigen Disziplin entwickelt. Nichtsdestoweniger ist die Analysis eines ihrer wichtigsten Anwendungsgebiete und kein Ana- lytiker kann heute ohne ihre Methoden auskommen. SchlieS- lich bildet die allgemeine Topologie selbst ein wichtiges Anwendungsbeispiel fUr die immer gr5Sere Bedeutung erlan- gende Kategorientheorie. Dennoch sind erst in jUngster Zeit in der allgemeinen Topologie kategorientheoretische Methoden zur Anwendung gekommen. Auf diesem Sektor liegt heute ein SchlUssel fUr weitere Forschungsarbeit. Es ware viel gewonnen, wenn das vorliegende Buch auch in dieser Richtung anregen wtirde. Der Begriff der gleich- maBigen Stetigkeit kann erst in einem spateren Kapitel des Buches im Rahmen der Theorie der uniformen Raume 2 (und der Proximit tsr ume) behandelt werden. Dort wird dann auch auf eln wichtlges Anwendungsbeisplel fUr uniforme R ume, n 11ch auf die topolog1schen Gruppen, kurz elngegangen. 0. 2. Mengentheoretlsche Grundbegrlffe 0. 2. 1. Bemerkung: In der auf Cantor zurUckgehenden naiven Mengenlehre wurde zun chst jede Zusammenfassung von'Objekten eine Menge genannt.


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Product Details
  • ISBN-13: 9783540074274
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 0002-2., Korr. Aufl.
  • Language: German
  • Returnable: Y
  • Spine Width: 26 mm
  • Width: 170 mm
  • ISBN-10: 3540074279
  • Publisher Date: 01 Jan 1976
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 490
  • Series Title: Hochschultext
  • Weight: 847 gr


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