Book Description
Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
Author : Niel Shell
Publisher : CRC Press
Page : 256 pages
File Size : 25,99 MB
Release : 2021-06-23
Category : Mathematics
ISBN : 1000444791
Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
Author : S. Warner
Publisher : Elsevier
Page : 579 pages
File Size : 50,36 MB
Release : 1989-06-01
Category : Mathematics
ISBN : 0080872689
Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.
Author : K.P. Hart
Publisher : Elsevier
Page : 537 pages
File Size : 35,8 MB
Release : 2003-11-18
Category : Mathematics
ISBN : 0080530869
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Author : Jose M. Bayod
Publisher : CRC Press
Page : 256 pages
File Size : 24,6 MB
Release : 2020-12-17
Category : Mathematics
ISBN : 1000154165
"Written by accomplished and well-known researchers in the field, this unique volume discusses important research topics on p-adic functional analysis and closely related areas, provides an authoritative overview of the main investigative fronts where developments are expected in the future, and more. "
Author : Theodore A. Bick
Publisher : CRC Press
Page : 274 pages
File Size : 48,60 MB
Release : 1993-02-17
Category : Mathematics
ISBN : 9780824788995
This textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques, centering on the concept of orthonormal sets of functions as generalizations of the trigonometric functions. To reinforce important concepts, the book contains exercises that range in difficulty from routine applications of the material just covered to extensions of that material.;Emphasizing the unifying nature of the material, this book: constructs physical models for both bounded and unbounded domains using rectangular and other co-ordinate systems; develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's employing Sturm-Liouville ststems as the primary vehicle; and presents illustrative examples in science and engineering, such as versions of the wave, diffusion equations and Laplace's equations.;Providing fundamental definitions for students with no prior experience in this topic other than differential equations, this text is intended as a resource for upper-level undergraduates in mathematics, physics and engineering, and students on courses on boundary value problems.
Author : H. Salzmann
Publisher : Cambridge University Press
Page : 418 pages
File Size : 30,72 MB
Release : 2007-08-23
Category : Mathematics
ISBN : 0521865166
The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
Author : Yau-Chuen Wong
Publisher : Routledge
Page : 442 pages
File Size : 20,82 MB
Release : 2019-01-25
Category : Mathematics
ISBN : 1351436457
This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.
Author : M. Ursul
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 31,41 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401002495
Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts.
Author : John Knopfmacher
Publisher : CRC Press
Page : 418 pages
File Size : 18,19 MB
Release : 2001-04-10
Category : Mathematics
ISBN : 0203908155
"Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory" offers a discussion of the advances and developments in the field of number theory arising from finite fields. It emphasizes mean-value theorems of multiplicative functions, the theory of additive formulations, and the normal distribution of values from additive functions
Author : Anatoly Kochubei
Publisher : CRC Press
Page : 344 pages
File Size : 36,32 MB
Release : 2001-08-03
Category : Mathematics
ISBN : 9780203908167
Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat