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

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. Front Matter....Pages N1-vii Introduction and historical remarks....Pages 1-19 Real numbers....Pages 21-47 Metric spaces....Pages 49-93 Continuous functions....Pages 95-128 Literature....Pages 129-133 Back Matter....Pages 134-136