The Continuum: A Constructive Approach to Basic Concepts of Real Analysis - Couverture souple

Taschner, Rudolf

Couverture souple

ISBN 10 : 3322820386 ISBN 13 : 9783322820389

Editeur : Vieweg+Teubner Verlag, 2012

Synopsis

Das Buch ist gut geeignet als Textgrundlage für Seminare aus reeller Analysis (vorzugsweise für Seminare, nachdem die Studierenden den üblichen formal-axiomatischen Zugang zu den reellen Zahlen erfahren haben).

In this small text the basic theory of the continuum, including the elements of metric space theory and continuity is developed within the system of intuitionistic mathematics in the sense of L.E.J. Brouwer and H. Weyl. The main features are proofs of the famous theorems of Brouwer concerning the continuity of all functions that are defined on "whole" intervals, the uniform continuity of all functions that are defined on compact intervals, and the uniform convergence of all pointwise converging sequences of functions defined on compact intervals. The constructive approach is interesting both in itself and as a contrast to, for example, the formal axiomatic one.

A propos du livre

À propos de l'auteur

Rudolf Taschner is Professor of Mathematics at the "Institute for Analysis and Scientific Computing", Technical University Vienna, Austria. In his recent book "Der Zahlen gigantische Schatten" (Vieweg 2004) he describes how intensively numbers penetrate the aspects of our life, and how far the "shadows of numbers" reach.

Détails de l'édition

• Éditeur: Vieweg+Teubner Verlag
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 3322820386
• ISBN 13: 9783322820389
• Reliure: Broché
• Nombre de pages: 152
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; Allemagne