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## ＜図書＞Introduction to the analysis of metric spaces

責任表示 J.R. Giles Australian Mathematical Society lecture series ; 3 図書 Cambridge [Cambridgeshire] : Cambridge University Press 1987 英語 xiv, 257 p. : ill. ; 24 cm Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fun...amental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated. Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated. 続きを見る

### 書誌詳細

一般注記 Includes index LCSH:Metric spacesLCSH:Normed linear spacesLCSH:Functional analysis LCC:QA611.28DC19:514/.3 1001390549 0521350514 BA01317356 ISBN:0521350514: pbk. ; ISBN:0521359287 2009.11.02 2009.11.02