Sinopsis
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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Acerca del autor
Rudolf Taschner is Professor of Mathematics at the "Institute for Analysis and Scientific Computing", Technical University Vienna, Austria. In his recent book "Der Zahlen gigantische Schatten" (Vieweg 2004) he describes how intensively numbers penetrate the aspects of our life, and how far the "shadows of numbers" reach.
De la contraportada
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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The Continuum A Constructive A
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Vieweg+Teubner Verlag, 2005
ISBN 10: 3834800406
ISBN 13: 9783834800404
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The Continuum : A Constructive Approach to some Basic Concepts of Real Analysis
Publicado por
Vieweg+Teubner Verlag, 2005
ISBN 10: 3834800406
ISBN 13: 9783834800404
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