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

By: Taschner, Rudolf [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Wiesbaden : Vieweg+Teubner Verlag, 2005.Description: XI, 136 p. 8 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783322820365.Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Mathematics | AnalysisDDC classification: 515 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK6381
Total holds: 0

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.

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.

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