Metric Spaces

Metric Spaces
Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
Total Pages: 318
Release: 2006-12-26
Genre: Mathematics
ISBN: 1846286271

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.

Lectures on Analysis on Metric Spaces

Lectures on Analysis on Metric Spaces
Author: Juha Heinonen
Publisher: Springer Science & Business Media
Total Pages: 158
Release: 2001
Genre: Mathematics
ISBN: 9780387951041

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Metric Spaces

Metric Spaces
Author: Satish Shirali
Publisher: Springer Science & Business Media
Total Pages: 238
Release: 2006
Genre: Mathematics
ISBN: 9781852339227

One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily

Topology of Metric Spaces

Topology of Metric Spaces
Author: S. Kumaresan
Publisher: Alpha Science Int'l Ltd.
Total Pages: 172
Release: 2005
Genre: Computers
ISBN: 9781842652503

"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.

Metric Spaces of Non-Positive Curvature

Metric Spaces of Non-Positive Curvature
Author: Martin R. Bridson
Publisher: Springer Science & Business Media
Total Pages: 665
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662124947

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.

Set Theory and Metric Spaces

Set Theory and Metric Spaces
Author: Irving Kaplansky
Publisher: American Mathematical Society
Total Pages: 140
Release: 2020-09-10
Genre: Mathematics
ISBN: 1470463849

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.

Introduction to Metric and Topological Spaces

Introduction to Metric and Topological Spaces
Author: Wilson A Sutherland
Publisher: Oxford University Press
Total Pages: 219
Release: 2009-06-18
Genre: Mathematics
ISBN: 0191568309

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.

Metric Spaces

Metric Spaces
Author: Victor Bryant
Publisher: Cambridge University Press
Total Pages: 116
Release: 1985-05-02
Genre: Mathematics
ISBN: 9780521318976

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

Elements of Metric Spaces

Elements of Metric Spaces
Author: Manabendra Nath Mukherjee
Publisher: Academic Publishers
Total Pages: 216
Release: 2010
Genre: Metric spaces
ISBN: 9788189781989

Real Variables with Basic Metric Space Topology

Real Variables with Basic Metric Space Topology
Author: Robert B. Ash
Publisher: Courier Corporation
Total Pages: 216
Release: 2014-07-28
Genre: Mathematics
ISBN: 0486151492

Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.