Topological Spaces

Including a Treatment of Multi-valued Functions, Vector Spaces, and Convexity

Author: Claude Berge

Publisher: Courier Corporation

ISBN: 9780486696539

Category: Mathematics

Page: 270

View: 3010

Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.
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Topological Spaces

From Distance to Neighborhood

Author: Gerard Buskes,Arnoud van Rooij

Publisher: Springer Science & Business Media

ISBN: 1461206650

Category: Mathematics

Page: 313

View: 5820

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
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Modern Methods in Topological Vector Spaces

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 0486493539

Category: Mathematics

Page: 298

View: 3770

"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--
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Topology

Author: Klaus Jänich

Publisher: Springer

ISBN: 9781461270188

Category: Mathematics

Page: 193

View: 2408

Contents: Introduction. - Fundamental Concepts. - Topological Vector Spaces.- The Quotient Topology. - Completion of Metric Spaces. - Homotopy. - The Two Countability Axioms. - CW-Complexes. - Construction of Continuous Functions on Topological Spaces. - Covering Spaces. - The Theorem of Tychonoff. - Set Theory (by T. Br|cker). - References. - Table of Symbols. -Index.
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Combinatorial Optimization

Algorithms and Complexity

Author: Christos H. Papadimitriou,Kenneth Steiglitz

Publisher: Courier Corporation

ISBN: 0486320138

Category: Mathematics

Page: 528

View: 4445

This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.
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Topological Vector Spaces and Distributions

Author: John Horvath

Publisher: Courier Corporation

ISBN: 0486311031

Category: Mathematics

Page: 464

View: 9722

"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.
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Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 6214

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
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Advanced Calculus

Revised

Author: Lynn Harold Loomis,Shlomo Sternberg

Publisher: World Scientific Publishing Company

ISBN: 9814583952

Category: Mathematics

Page: 596

View: 9042

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
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Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes

Publisher: Courier Corporation

ISBN: 0486142272

Category: Technology & Engineering

Page: 576

View: 5118

Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.
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A Course of Modern Analysis

An Introduction to the General Theory of Infinite Series and of Analytic Functions, with an Account of the Principal Transcendental Functions

Author: Edmund Taylor Whittaker

Publisher: N.A

ISBN: N.A

Category: Calculus

Page: 378

View: 3267

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AB Bookman's Weekly

For the Specialist Book World

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Antiquarian booksellers

Page: N.A

View: 7464

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Existence Theorems for Ordinary Differential Equations

Author: Francis J. Murray,Kenneth S. Miller

Publisher: Courier Corporation

ISBN: 0486154955

Category: Mathematics

Page: 176

View: 6981

This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.
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Convex Optimization in Normed Spaces

Theory, Methods and Examples

Author: Juan Peypouquet

Publisher: Springer

ISBN: 3319137107

Category: Mathematics

Page: 124

View: 5774

This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.
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Real Analysis with Real Applications

Author: Kenneth R. Davidson,Allan P. Donsig

Publisher: N.A

ISBN: 9780130416476

Category: Mathematics

Page: 624

View: 2360

For one/two-semester undergraduate courses in real analysis. Using a progressive but flexible format, this text develops the principles of real analysis and shows how they can be used in a wide variety of applications.
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Analysis in Euclidean Space

Author: Kenneth Hoffman

Publisher: Courier Corporation

ISBN: 0486135845

Category: Mathematics

Page: 448

View: 7995

Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.
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Scalar and Asymptotic Scalar Derivatives

Theory and Applications

Author: George Isac,Sándor Zoltán Németh

Publisher: Springer Science & Business Media

ISBN: 0387739882

Category: Mathematics

Page: 245

View: 6396

This extremely useful book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. The text is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.
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Geometric and Topological Inference

Author: Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec

Publisher: Cambridge University Press

ISBN: 1108419399

Category: Computers

Page: 300

View: 846

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
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Uniform Distribution of Sequences

Author: L. Kuipers,H. Niederreiter

Publisher: Courier Corporation

ISBN: 0486149994

Category: Mathematics

Page: 416

View: 575

The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition.
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