000			02862nam a22004215i 4500
001			978-3-322-82036-5
003			DE-He213
005			20161121230931.0
007			cr nn 008mamaa
008			121227s2005 gw | s |||| 0|eng d
020			_a9783322820365 _9978-3-322-82036-5
024	7		_a10.1007/978-3-322-82036-5 _2doi
050		4	_aQA299.6-433
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515 _223
100	1		_aTaschner, Rudolf. _eauthor.
245	1	4	_aThe Continuum _h[electronic resource] : _bA Constructive Approach to Basic Concepts of Real Analysis / _cby Rudolf Taschner.
264		1	_aWiesbaden : _bVieweg+Teubner Verlag, _c2005.
300			_aXI, 136 p. 8 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_a1 Introduction and historical remarks -- 1.1 Farey fractions -- 1.2 The pentagram -- 1.3 Continued fractions -- 1.4 Special square roots -- 1.5 Dedekind cuts -- 1.6 Weyl’s alternative -- 1.7 Brouwer’s alternative -- 1.8 Integration in traditional and in intuitionistic framework -- 1.9 The wager -- 1.10 How to read the following pages -- 2 Real numbers -- 2.1 Definition of real numbers -- 2.2 Order relations -- 2.3 Equality and apartness -- 2.4 Convergent sequences of real numbers -- 3 Metric spaces -- 3.1 Metric spaces and complete metric spaces -- 3.2 Compact metric spaces -- 3.3 Topological concepts -- 3.4 The s-dimensional continuum -- 4 Continuous functions -- 4.1 Pointwise continuity -- 4.2 Uniform continuity -- 4.3 Elementary calculations in the continuum -- 4.4 Sequences and sets of continuous functions -- 5 Literature.
520			_aIn 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.
650		0	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aAnalysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783322820389
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-322-82036-5
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506094 _d506094