# Search Results for "metric-spaces"

## Metric Spaces

**Author**: Mícheál O'Searcoid**Publisher:**Springer Science & Business Media**ISBN:**9781846286278**Category:**Mathematics**Page:**304**View:**7854

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,Harkrishan Lal Vasudeva**Publisher:**Springer Science & Business Media**ISBN:**9781852339227**Category:**Mathematics**Page:**222**View:**4643

Since the last century, the postulational method and an abstract point of view have played a vital role in the development of modern mathematics. The experience gained from the earlier concrete studies of analysis point to the importance of passage to the limit. The basis of this operation is the notion of distance between any two points of the line or the complex plane. The algebraic properties of underlying sets often play no role in the development of analysis; this situation naturally leads to the study of metric spaces. The abstraction not only simplifies and elucidates mathematical ideas that recur in different guises, but also helps eco- mize the intellectual effort involved in learning them. However, such an abstract approach is likely to overlook the special features of particular mathematical developments, especially those not taken into account while forming the larger picture. Hence, the study of particular mathematical developments is hard to overemphasize. The language in which a large body of ideas and results of functional analysis are expressed is that of metric spaces. The books on functional analysis seem to go over the preliminaries of this topic far too quickly. The present authors attempt to provide a leisurely approach to the theory of metric spaces. In order to ensure that the ideas take root gradually but firmly, a large number of examples and counterexamples follow each definition. Also included are several worked examples and exercises. Applications of the theory are spread out over the entire book.

## Elements of Metric Spaces

**Author**: N.A**Publisher:**Academic Publishers**ISBN:**9788189781989**Category:**Metric spaces**Page:**204**View:**3144

## Probabilistic Metric Spaces

**Author**: B. Schweizer,A. Sklar**Publisher:**Courier Corporation**ISBN:**0486143759**Category:**Mathematics**Page:**336**View:**8886

This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.

## Metric Spaces

*Iteration and Application*

**Author**: Victor Bryant**Publisher:**Cambridge University Press**ISBN:**9780521318976**Category:**Mathematics**Page:**104**View:**9822

An introduction to metric spaces for those interested in the applications as well as theory.

## Lectures on Analysis on Metric Spaces

**Author**: Juha Heinonen,Assistant Professor of Mathematics Juha Heinonen**Publisher:**Springer Science & Business Media**ISBN:**9780387951041**Category:**Mathematics**Page:**140**View:**9001

Studies basic covering theorems and their applications to analysis in metric measure spaces. This book discusses Sobolev spaces emphasizing principles that are valid in larger contexts. It also presents a basic theory of quasisymmetric maps between metric spaces.

## Metric Spaces of Fuzzy Sets: Theory and Applications

**Author**: Phil Diamond,Peter Kloeden**Publisher:**World Scientific**ISBN:**9814518115**Category:**Computers**Page:**188**View:**3328

The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ℜn. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis. This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis. Contents:Fuzzy SetsSpaces of Subsets of ℜnCompact Convex Subsets of ℜnSet Valued MappingsCrisp GeneralizationsThe Space εnMetrics on εnCompactness CriteriaGeneralizationsFuzzy Set Valued Mappings of Real VariablesFuzzy Random VariablesComputational MethodsFuzzy Differential EquationsOptimization Under UncertaintyFuzzy Iterations and Image Processing Readership: Mathematicians and computer scientists. keywords:Metric Spaces;Multifunctions;Fuzzy Sets;Fuzzy Data Fitting;Fuzzy Dynamical Systems;Iterated Fuzzy Systems “… is a valuable addition to the literature about fuzzy analysis, leading the reader to the edge of current research.” Mathematical Reviews “… the book seems to be the only, and thus valuable, source of mathematical concepts and results on fuzzy sets and functions, which are presented in a clear, and quite rigorous, format.” Journal of Classification

## Metric Spaces

**Author**: E. T. Copson**Publisher:**CUP Archive**ISBN:**9780521357326**Category:**Mathematics**Page:**152**View:**3991

Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.

## Set Theory and Metric Spaces

**Author**: Irving Kaplansky**Publisher:**American Mathematical Soc.**ISBN:**0821826948**Category:**Mathematics**Page:**140**View:**1083

This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. ... There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem ... The presentation of metric spaces before topological spaces ... should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. --Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. -- Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

## 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:**4564

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