The Continuum: A Constructive Approach to Basic Concepts of Real Analysis (Paperback)

The Continuum: A Constructive Approach to Basic Concepts of Real Analysis By Rudolf Taschner Cover Image

The Continuum: A Constructive Approach to Basic Concepts of Real Analysis (Paperback)

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Das Buch ist gut geeignet als Textgrundlage f r Seminare aus reeller Analysis (vorzugsweise f r Seminare, nachdem die Studierenden den blichen 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.
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.
Product Details ISBN: 9783322820389
ISBN-10: 3322820386
Publisher: Vieweg+teubner Verlag
Publication Date: February 5th, 2012
Pages: 136
Language: English