The Continuum
A Constructive Approach to Basic Concepts of Real Analysis
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Beschreibung
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.
Das Buch ist gut geeignet als Textgrundlage für Seminare aus reeller Analysis (vorzugsweise für Seminare, nachdem die Studierenden den üblichen formal-axiomatischen Zugang zu den reellen Zahlen erfahren haben).
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.
A constructive approach to Real Analysis
Autor*in
Rudolf Taschner
Themen in »The Continuum«
Brouwer Continuous Functions Metric Spaces Real Numbers Weyl calculus real analysis