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© 2005

The Continuum

A Constructive Approach to Basic Concepts of Real Analysis

Textbook

Table of contents

  1. Front Matter
    Pages N1-vii
  2. Rudolf Taschner
    Pages 1-19
  3. Rudolf Taschner
    Pages 21-47
  4. Rudolf Taschner
    Pages 49-93
  5. Rudolf Taschner
    Pages 95-128
  6. Rudolf Taschner
    Pages 129-133
  7. Back Matter
    Pages 134-136

About this book

Introduction

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.

Keywords

Brouwer Continuous Functions Metric Spaces Real Numbers Weyl calculus real analysis

Authors and affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

About the authors

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.

Bibliographic information

  • Book Title The Continuum
  • Book Subtitle A Constructive Approach to Basic Concepts of Real Analysis
  • Authors Rudolf Taschner
  • DOI https://doi.org/10.1007/978-3-322-82036-5
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2005
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-8348-0040-4
  • Softcover ISBN 978-3-322-82038-9
  • eBook ISBN 978-3-322-82036-5
  • Edition Number 1
  • Number of Pages XI, 136
  • Number of Illustrations 8 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site