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 Browuer 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.

A publication of Vieweg Verlag. The AMS is exclusive distributor in North America. Vieweg Verlag Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Advanced undergraduate/graduate students and lecturers in Real Analysis.

Table of Contents

• Introduction and historical remarks
• Real numbers
• Metric spaces
• Continuous functions
• Literature
• Index