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Grundstrukturen Der Analysis I by W. Gähler

Grundstrukturen Der Analysis I

by W. Gähler
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Book cover type: Paperback
  • ISBN13: 9783764309015
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 412
  • Original Price: EUR 56.07
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 672 grams
  • BISAC Subject(s): General

In der Monographie wird ein systematischer Aufbau der Analysis unter Be- nutzung des Limitierungsbegriffs vorgenommen. Insbesondere werden die Theorie der Limesräume und limesuniformen Räume, die limitierte Algebra und die allgemeine Differentialrechnung entwickelt. Die Notwendigkeit, den Topologiebegriff abzuschwächen und ihn durch den - wie sich zeigt - bedeutend leistungsfähigeren Begriff der Limitierung zu ersetzen, ergibt sich bei einer Reihe von Problemen in Abbildungsräumen. Wir führen zwei Beispiele an. Bekanntlich existiert zu topologischen, ja sogar zu separierten topologischen Räumen X und Y im allgemeinen keine gröbste Topologie von C(X, Y), bezüglich der die Evaluationsabbildung w von C(X, Y) X X in Y stetig ist, was zur Folge hat, da die Kategorien aller topologischen Räume und aller HAusDoRFF-Räume nicht cartesisch abge- schlossen sind. Es existiert aber stets eine gröbste Limitierung von C(X, Y), bezüglich der w stetig ist, und die Kategorien aller pseudotopologischen und aller separierten pseudotopologischen Räume sind cartesisch abgeschlossen. Nach dem Satz von KELLER-MAISSEN gibt es zu separierten lokalkonvexen topologischen Vektorräumen X und Y nur dann eine Vektorraumtopologie von L(X, Y), bezüglich der die Evaluationsabbildung von L(X, Y) X X in Y stetig ist, wenn X normierbar ist, weshalb zum Beispiel die Kategorien aller topologischen Vektorräume und aller separierten lokalkonvexen topolo- gischen Vektorräume bezüglich Tensorprodukte keine abgeschlossenen Kate- gorien bilden. Die Kategorien aller pseudotopologischen Vektorräume und aller in einem engeren Sinne separierten lokalkonvexen pseudotopologischen Vektorräume sind hingegen, als symmetrische monoidale Kategorien bezüglich Tensorprodukte, abgeschlossen.

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