The Continuum
Subtitle: A Constructive Approach to Basic Concepts of Real Analysis
By: by Rudolf Taschner
Publisher: Vieweg+Teubner Verlag
Published: 2005
Place of publication: Wiesbaden
Language: eng
Format: [electronic resource] :
Number of pages: 136
ISBN-13: 9783322820365
Subjects: Mathematics; Global analysis (Mathematics)
Description: 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.