Search results for: metric-spaces

Metric Spaces

Author : Mícheál O'Searcoid
File Size : 81.3 MB
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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.

Metric Spaces

Author : Satish Shirali
File Size : 78.82 MB
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One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily

Introduction to the Analysis of Metric Spaces

Author : John R. Giles
File Size : 71.59 MB
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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.

Neutrosophic Metric Spaces

Author : Murat Kirisci
File Size : 49.25 MB
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In present paper, the definition of new metric space with neutrosophic numbers is given. Several topological and structural properties have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic metric spaces.

Elements of Metric Spaces

Author : Manabendra Nath Mukherjee
File Size : 89.35 MB
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Metric Spaces

Author : E. T. Copson
File Size : 76.94 MB
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Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

Metric Spaces Convexity and Nonpositive Curvature

Author : Athanase Papadopoulos
File Size : 21.52 MB
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This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to the theory of geodesics in metric spaces, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples from classical hyperbolic geometry and from the theory of Teichmuller spaces. The book is useful for students and researchers in geometry, topology and analysis.

Metric Spaces

Author : Victor Bryant
File Size : 87.99 MB
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An introduction to metric spaces for those interested in the applications as well as theory.

An Introduction to Metric Spaces and Fixed Point Theory

Author : Mohamed A. Khamsi
File Size : 61.30 MB
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Presents up-to-date Banach space results. * Features an extensive bibliography for outside reading. * Provides detailed exercises that elucidate more introductorymaterial.

Metric Space

Author : S.C. Sharma
File Size : 80.76 MB
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This book Metric Space has been written for the students of various universities. In the earlier chapters, proof are given in considerable detail, as our subject unfolds through the successive chapters and the reader acquires experience in following abstract mathematical arguments, the proof become briefer and minor details are more and more left for the reader to fill in for himself. It is a basic principle in the study of mathematics, and one too seldom emphasised that a proof is not really understood until the stage is reached at which one can grasp it is a whole and see it as a single idea. In achieving this end much more is necessary than merely following the individual steps in the reasoning. Contents: Basic Concept of Set, Metric Space, Compactness.