Topology Of Metric Spaces
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Topology Of Metric Spaces
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Author : S. Kumaresan
language : en
Publisher: Alpha Science Int'l Ltd.
Release Date : 2005
Topology Of Metric Spaces written by S. Kumaresan and has been published by Alpha Science Int'l Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
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.
Introduction To The Analysis Of Metric Spaces
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Author : John R. Giles
language : en
Publisher: Cambridge University Press
Release Date : 1987-09-03
Introduction To The Analysis Of Metric Spaces written by John R. Giles 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 1987-09-03 with Mathematics categories.
Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.
Introduction To Metric And Topological Spaces
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Author : Wilson Alexander Sutherland
language : en
Publisher: Oxford University Press
Release Date : 1975
Introduction To Metric And Topological Spaces written by Wilson Alexander 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 1975 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 book 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. The book is aimed primarily at the second-year mathematics student, and numerous exercises are included.
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
Topological Spaces
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Author : Gerard Buskes
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-15
Topological Spaces written by Gerard Buskes 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 1997-08-15 with Mathematics categories.
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.
Metric Space Topology Examples Exercises And Solutions
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Author : Wing-sum Cheung
language : en
Publisher: World Scientific
Release Date : 2023-10-18
Metric Space Topology Examples Exercises And Solutions written by Wing-sum Cheung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Mathematics categories.
This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.The learning outcomes include:
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 : Satish Shirali
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-16
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 2005-12-16 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
Multivariable Analysis
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Author : Satish Shirali
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-13
Multivariable Analysis 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 2010-12-13 with Mathematics categories.
This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.