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The classical fields [struc...
The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work
Monografía
monografia Rebiun28700837 https://catalogo.rebiun.org/rebiun/record/Rebiun28700837 m o d | cr -n--------- 071115s2007 enk ob 001 0 eng d 2007282003 1-139-88331-3 1-107-38402-8 1-107-38753-1 0-511-82626-5 1-107-39886-X 0-511-72150-1 1-107-39045-1 1-107-39525-9 UPVA 998450335703706 UAM 991008030683204211 CBUC 991010752617006709 MiAaPQ MiAaPQ MiAaPQ eng 512.74 The classical fields electronic resource] structural features of the real and rational numbers H. Salzmann ... [et al.]. Cambridge New York Cambridge University Press 2007 Cambridge New York Cambridge New York Cambridge University Press 1 online resource (419 p.) 1 online resource (419 p.) Text txt computer c online resource cr Encyclopedia of mathematics and its applications v. 112 Description based upon print version of record Includes bibliographical references and index Cover; Half-title; Title; Copyright; Contents; Preface; Notation; 1 Real numbers; 1 The additive group of real numbers; 2 The multiplication of real numbers, with a digression on fields; 3 The real numbers as an ordered set; 4 Continued fractions; 5 The real numbers as a topological space; Characterizing the real line, the arc, and the circle; Independence of characteristic properties; Subspaces and continuous images of the real line; Homeomorphisms of the real line; Weird topologies on the real line; 6 The real numbers as a field; 7 The real numbers as an ordered group 8 The real numbers as a topological groupSubgroups and quotients; Characterizations; A counter-example; Automorphisms and endomorphisms; Groups having an endomorphism field; 9 Multiplication and topology of the real numbers; 10 The real numbers as a measure space; 11 The real numbers as an ordered field; 12 Formally real and real closed fields; 13 The real numbers as a topological field; 14 The complex numbers; 2 Non-standard numbers; 21 Ultraproducts; 22 Non-standard rationals; 23 A construction of the real numbers; 24 Non-standard reals; Ordering and topology; (Sj(B1-fields 25 Continuity and convergence26 Topology of the real numbers in non-standard terms; 27 Differentiation; 28 Planes and fields; 3 Rational numbers; 31 The additive group of the rational numbers; 32 The multiplication of the rational numbers; 33 Ordering and topology of the rational numbers; 34 The rational numbers as a field; 35 Ordered groups of rational numbers; 36 Addition and topologies of the rational numbers; 37 Multiplication and topologies of the rational numbers; 4 Completion; 41 Completion of chains; 42 Completion of ordered groups and fields 43 Completion of topological abelian groups44 Completion of topological rings and fields; 5 The p-adic numbers; 51 The field of p-adic numbers; 52 The additive group of p-adic numbers; 53 The multiplicative group of p-adic numbers; 54 Squares of p-adic numbers and quadratic forms; 55 Absolute values; 56 Valuations; 57 Topologies of valuation type; 58 Local fields and locally compact fields; 6 Appendix; 61 Ordinals and cardinals; 62 Topological groups; 63 Locally compact abelian groups and Pontryagin duality; 64 Fields; Hints and solutions; References; Index The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work English Numbers, Real Numbers, Rational Number theory Electronic books Salzmann, Hubert 1861-1910) 0-521-86516-6 1-299-90922-1 Encyclopedia of mathematics and its applications v. 112