The Continuum A Constructive Approach to Basic Concepts of Real Analysis /

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 co...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Taschner, Rudolf (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag, 2005.
Édition:1st ed. 2005.
Sujets:
Mathematical analysis.
Analysis.
Accès en ligne:Texto Completo
Table des matières:
  • 1 Introduction and historical remarks
  • 1.1 Farey fractions
  • 1.2 The pentagram
  • 1.3 Continued fractions
  • 1.4 Special square roots
  • 1.5 Dedekind cuts
  • 1.6 Weyl's alternative
  • 1.7 Brouwer's alternative
  • 1.8 Integration in traditional and in intuitionistic framework
  • 1.9 The wager
  • 1.10 How to read the following pages
  • 2 Real numbers
  • 2.1 Definition of real numbers
  • 2.2 Order relations
  • 2.3 Equality and apartness
  • 2.4 Convergent sequences of real numbers
  • 3 Metric spaces
  • 3.1 Metric spaces and complete metric spaces
  • 3.2 Compact metric spaces
  • 3.3 Topological concepts
  • 3.4 The s-dimensional continuum
  • 4 Continuous functions
  • 4.1 Pointwise continuity
  • 4.2 Uniform continuity
  • 4.3 Elementary calculations in the continuum
  • 4.4 Sequences and sets of continuous functions
  • 5 Literature.

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