A Comprehensive Textbook On Metric Spaces
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A Comprehensive Textbook On Metric Spaces
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Author : Surinder Pal Singh Kainth
language : en
Publisher: Springer Nature
Release Date : 2023-10-30
A Comprehensive Textbook On Metric Spaces written by Surinder Pal Singh Kainth and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Mathematics categories.
This textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.
A Comprehensive Textbook On Metric Spaces
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Author : Surinder Pal Singh Kainth
language : en
Publisher:
Release Date : 2024-11
A Comprehensive Textbook On Metric Spaces written by Surinder Pal Singh Kainth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11 with Mathematics categories.
Metric Spaces
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Author : Satish Shirali
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
Metric Spaces written by Satish Shirali and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Metric Spaces
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Author : Mícheál O'Searcoid
language : en
Publisher: Springer
Release Date : 2006-09-08
Metric Spaces written by Mícheál O'Searcoid and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-08 with Mathematics categories.
The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
Lectures On Analysis On Metric Spaces
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Author : Juha Heinonen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Analysis On Metric Spaces written by Juha Heinonen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar. The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.
A Comprehensive Textbook Of Classical Mathematics
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Author : H.B. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
A Comprehensive Textbook Of Classical Mathematics written by H.B. Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree.
Real Variables With Basic Metric Space Topology
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Author : Robert B. Ash
language : en
Publisher: Courier Corporation
Release Date : 2014-07-28
Real Variables With Basic Metric Space Topology written by Robert B. Ash and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-28 with Mathematics categories.
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
Metric Spaces
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Author : Victor Bryant
language : en
Publisher: Cambridge University Press
Release Date : 1985-05-02
Metric Spaces written by Victor Bryant and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-02 with Mathematics categories.
An introduction to metric spaces for those interested in the applications as well as theory.
Introduction To Metric And Topological Spaces
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Author : Wilson A Sutherland
language : en
Publisher: Oxford University Press
Release Date : 2009-06-18
Introduction To Metric And Topological Spaces written by Wilson A Sutherland and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-18 with Mathematics categories.
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
An Introduction To Metric Spaces And Fixed Point Theory
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Author : Mohamed A. Khamsi
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
An Introduction To Metric Spaces And Fixed Point Theory written by Mohamed A. Khamsi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.