Introduction to Metric and Topological Spaces

DOWNLOAD NOW »

Author: Wilson Alexander Sutherland,W. A. Sutherland

Publisher: Oxford University Press

ISBN: 9780198531616

Category: Science

Page: 181

View: 8663

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

DOWNLOAD NOW »

Author: Wilson A Sutherland

Publisher: Oxford University Press

ISBN: 0191568309

Category: Mathematics

Page: N.A

View: 6806

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

Third Edition

DOWNLOAD NOW »

Author: Bert Mendelson

Publisher: Courier Corporation

ISBN: 0486135098

Category: Mathematics

Page: 224

View: 1721

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 the Analysis of Metric Spaces

DOWNLOAD NOW »

Author: John R. Giles,John Robilliard Giles

Publisher: Cambridge University Press

ISBN: 9780521359283

Category: Mathematics

Page: 257

View: 4408

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.

A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable

DOWNLOAD NOW »

Author: D. J. H. Garling

Publisher: Cambridge University Press

ISBN: 1107355427

Category: Mathematics

Page: N.A

View: 2132

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

An Introduction to Metric Spaces and Fixed Point Theory

DOWNLOAD NOW »

Author: Mohamed A. Khamsi,William A. Kirk

Publisher: John Wiley & Sons

ISBN: 1118031326

Category: Mathematics

Page: 320

View: 6550

Presents up-to-date Banach space results. * Features an extensive bibliography for outside reading. * Provides detailed exercises that elucidate more introductorymaterial.

Metrics, Norms and Integrals

An Introduction to Contemporary Analysis

DOWNLOAD NOW »

Author: J. J. Koliha

Publisher: World Scientific

ISBN: 981283656X

Category: Mathematics

Page: 408

View: 8361

Metrics, Norms and Integrals is a textbook on contemporary analysis based on the author's lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.

A First Course in Topology

An Introduction to Mathematical Thinking

DOWNLOAD NOW »

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486780015

Category: Mathematics

Page: 272

View: 3898

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

Introduction to Uniform Spaces

DOWNLOAD NOW »

Author: I. M. James

Publisher: Cambridge University Press

ISBN: 9780521386203

Category: Mathematics

Page: 148

View: 674

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.