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Author: Satish Shirali
Publisher: Springer Science & Business Media
Published: 2006
Total Pages: 238
ISBN-13: 9781852339227
DOWNLOAD EBOOK →One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
Published: 2006-12-26
Total Pages: 318
ISBN-13: 1846286271
DOWNLOAD EBOOK →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.
Author: Victor Bryant
Publisher: Cambridge University Press
Published: 1985-05-02
Total Pages: 116
ISBN-13: 9780521318976
DOWNLOAD EBOOK →An introduction to metric spaces for those interested in the applications as well as theory.
Author: Martin R. Bridson
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 665
ISBN-13: 3662124947
DOWNLOAD EBOOK →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.
Author: Dhananjay Gopal
Publisher: CRC Press
Published: 2020-07-14
Total Pages: 303
ISBN-13: 1000087999
DOWNLOAD EBOOK →This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications. Some of the noteworthy features of this book include · Diagrammatic illustrations that encourage readers to think geometrically · Focus on systematic strategy to generate ideas for the proofs of theorems · A wealth of remarks, observations along with a variety of exercises · Historical notes and brief biographies appearing throughout the text
Author: S. Kumaresan
Publisher: Alpha Science Int'l Ltd.
Published: 2005
Total Pages: 172
ISBN-13: 9781842652503
DOWNLOAD EBOOK →"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.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
Published: 2008-10-29
Total Pages: 334
ISBN-13: 376438722X
DOWNLOAD EBOOK →The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Author: Juha Heinonen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 149
ISBN-13: 1461301319
DOWNLOAD EBOOK →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.
Author: Irving Kaplansky
Publisher: American Mathematical Society
Published: 2020-09-10
Total Pages: 140
ISBN-13: 1470463849
DOWNLOAD EBOOK →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.
Author: Wilson A Sutherland
Publisher: Oxford University Press
Published: 2009-06-18
Total Pages: 219
ISBN-13: 0191568309
DOWNLOAD EBOOK →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.
