# Search Results for "metric-spaces"

## Metric Spaces

**Author**: Mícheál O'Searcoid**Publisher:**Springer Science & Business Media**ISBN:**9781846286278**Category:**Mathematics**Page:**304**View:**9626

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:**1558

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.

## Metric Spaces

*Iteration and Application*

**Author**: Victor Bryant**Publisher:**Cambridge University Press**ISBN:**9780521318976**Category:**Mathematics**Page:**104**View:**5298

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

## Probabilistic Metric Spaces

**Author**: B. Schweizer,A. Sklar**Publisher:**Courier Corporation**ISBN:**0486143759**Category:**Mathematics**Page:**336**View:**7583

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

**Author**: E. T. Copson**Publisher:**CUP Archive**ISBN:**9780521357326**Category:**Mathematics**Page:**152**View:**4267

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

## Metric Spaces of Non-Positive Curvature

**Author**: Martin R. Bridson,André Häfliger**Publisher:**Springer Science & Business Media**ISBN:**9783540643241**Category:**Mathematics**Page:**643**View:**1569

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

## Topology of Metric Spaces

**Author**: S. Kumaresan**Publisher:**Alpha Science Int'l Ltd.**ISBN:**9781842652503**Category:**Mathematics**Page:**152**View:**3627

"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.

## 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:**5344

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

## Elements of Metric Spaces

**Author**: N.A**Publisher:**Academic Publishers**ISBN:**9788189781989**Category:**Metric spaces**Page:**204**View:**6655

## Set Theory and Metric Spaces

**Author**: Irving Kaplansky**Publisher:**American Mathematical Soc.**ISBN:**0821826948**Category:**Mathematics**Page:**140**View:**8647

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.