02842nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002400139245009400163250001700257260004800274300003200322505023800354653002400592653003200616653001900648653002000667653004000687710003400727041001900761989003800780490003400818856006100852082001000913520160500923EB000614973EBX0100000000000000046805500000000000000.0cr|||||||||||||||||||||140122 ||| eng a97803872262001 aBridges, Douglas S.00aFoundations of Real and Abstract AnalysishElektronische Ressourcecby Douglas S. Bridges a1st ed. 1998 aNew York, NYbSpringer New Yorkc1998, 1998 aXIV, 322 pbonline resource0 aReal Analysis -- Analysis on the Real Line -- Differentiation and the Lebesgue Integral -- Abstract Analysis -- Analysis in Metric Spaces -- Analysis in Normed Linear Spaces -- Hilbert Spaces -- An Introduction to Functional Analysis aOperations research aFunctions of real variables aReal Functions aDecision making aOperations Research/Decision Theory2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aGraduate Texts in Mathematics uhttps://doi.org/10.1007/b97625?nosfx=yxVerlag3Volltext0 a515.8 aThe core of this book, Chapters three through five, presents a course on metric, normed, and Hilbert spaces at the senior/graduate level. The motivation for each of these chapters is the generalisation of a particular attribute of the n Euclidean space R: in Chapter 3, that attribute is distance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem (3.3.12) showing that the Lebesgue covering property is equivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts of their mathematical studies, students contrive to avoid analysis courses at almost any cost, in particular that of their own educational and technical deprivation. Many universities have at times capitulated to the negative demand of students for analysis courses and have seriously watered down their expectations of students in that area. As a result, mathematics majors are graduating, sometimes with high honours, with little exposure to anything but a rudimentary course or two on real and complex analysis, often without even an introduction to the Lebesgue integral