MARC Record from harvard_bibliographic_metadata

LEADER: 02684nam a22003975a 4500
001 014158450-5
005 20141003190653.0
008 121227s2005 gw | o ||0| 0|eng d
020 $a9783322820365
020 $a9783322820389 (ebk.)
020 $a9783322820365
020 $a9783322820389
024 7 $a10.1007/978-3-322-82036-5$2doi
035 $a(Springer)9783322820365
040 $aSpringer
050 4 $aQA299.6-433
072 7 $aMAT034000$2bisacsh
072 7 $aPBK$2bicssc
082 04 $a515$223
100 1 $aTaschner, Rudolf,$eauthor.
245 14 $aThe Continuum :$bA Constructive Approach to Basic Concepts of Real Analysis /$cby Rudolf Taschner.
264 1 $aWiesbaden :$bVieweg+Teubner Verlag,$c2005.
300 $aXI, 136p. 8 illus.$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 10 $aMathematics.
650 0 $aGlobal analysis (Mathematics)
650 0 $aMathematics.
650 24 $aAnalysis.
776 08 $iPrinted edition:$z9783322820389
988 $a20140910
906 $0VEN