E Book

The Continuum

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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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Ketersediaan

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

: .,

Deskripsi Fisik

XI, 136 p. 8 illus.online resource.

Bahasa

English

ISBN/ISSN

9783322820365

Klasifikasi

515

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Mathematical analysis.
Analysis (Mathematics).
Analysis.

Info Detail Spesifik

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Pernyataan Tanggungjawab

by Rudolf Taschner.

Versi lain/terkait

Lampiran Berkas

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