Introduction to Metric and Topological Spaces

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Introduction to Metric and Topological Spaces

Introduction to Metric and Topological Spaces

  • Author: Wilson Alexander Sutherland,W. A. Sutherland
  • Publisher: Oxford University Press
  • ISBN: 9780198531616
  • Category: Science
  • Page: 181
  • View: 1033
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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.

Introduction to Metric and Topological Spaces

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Introduction to Metric and Topological Spaces

Introduction to Metric and Topological Spaces

  • Author: Wilson A Sutherland
  • Publisher: Oxford University Press
  • ISBN: 0191568309
  • Category: Mathematics
  • Page: N.A
  • View: 9945
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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 Topology

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Introduction to Topology

Introduction to Topology

Third Edition

  • Author: Bert Mendelson
  • Publisher: Courier Corporation
  • ISBN: 0486135098
  • Category: Mathematics
  • Page: 224
  • View: 6325
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Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Introduction to General Topology

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Introduction to General Topology

Introduction to General Topology

  • Author: K. D. Joshi
  • Publisher: New Age International
  • ISBN: 9780852264447
  • Category: Topology
  • Page: 412
  • View: 6548
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Introduction to the Analysis of Metric Spaces

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Introduction to the Analysis of Metric Spaces

Introduction to the Analysis of Metric Spaces

  • Author: John R. Giles,John Robilliard Giles
  • Publisher: Cambridge University Press
  • ISBN: 9780521359283
  • Category: Mathematics
  • Page: 257
  • View: 7843
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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.

Introduction to Set Theory and Topology

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Introduction to Set Theory and Topology

Introduction to Set Theory and Topology

  • Author: Kazimierz Kuratowski
  • Publisher: Elsevier
  • ISBN: 1483151638
  • Category: Mathematics
  • Page: 352
  • View: 2625
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Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Introduction to Topology

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Introduction to Topology

Introduction to Topology

Pure and Applied

  • Author: Colin Conrad Adams,Robert David Franzosa
  • Publisher: Prentice Hall
  • ISBN: N.A
  • Category: Mathematics
  • Page: 489
  • View: 5550
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For juniors and seniors of various majors, taking a first course in topology. This book introduces topology as an important and fascinating mathematics discipline. Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields.

Introduction to Uniform Spaces

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Introduction to Uniform Spaces

Introduction to Uniform Spaces

  • Author: I. M. James
  • Publisher: Cambridge University Press
  • ISBN: 9780521386203
  • Category: Mathematics
  • Page: 148
  • View: 6054
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This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Metric Space

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Metric Space

Metric Space

  • Author: S.C. Sharma
  • Publisher: Discovery Publishing House
  • ISBN: 9788183561181
  • Category: Metric spaces
  • Page: 300
  • View: 9876
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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.

An Introduction to Metric Spaces and Fixed Point Theory

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An Introduction to Metric Spaces and Fixed Point Theory

An Introduction to Metric Spaces and Fixed Point Theory

  • Author: Mohamed A. Khamsi,William A. Kirk
  • Publisher: John Wiley & Sons
  • ISBN: 1118031326
  • Category: Mathematics
  • Page: 320
  • View: 3767
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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.