Set Theory and Metric Spaces

Author: Irving Kaplansky
Publisher: American Mathematical Soc.
ISBN: 0821826948
Category: Mathematics
Page: 140
View: 1974
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.

Metric Spaces of Fuzzy Sets

Theory and Applications
Author: Phil Diamond,Peter E. Kloeden
Publisher: World Scientific
ISBN: 9789810217310
Category: Mathematics
Page: 178
View: 7240
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 ?n. 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.

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: 7780
Presents up-to-date Banach space results. * Features an extensive bibliography for outside reading. * Provides detailed exercises that elucidate more introductorymaterial.

Set theory and metric spaces

Author: Edwin Henry Spanier
Publisher: N.A
Category: Mathematics
Page: N.A
View: 8030

Metric Spaces

Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
ISBN: 9781846286278
Category: Mathematics
Page: 304
View: 7932
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.

Introduction to Set Theory and Topology

Author: Kazimierz Kuratowski
Publisher: Elsevier
ISBN: 1483151638
Category: Mathematics
Page: 352
View: 5801
Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Set Theory

Author: Felix Hausdorff
Publisher: American Mathematical Soc.
ISBN: 9780821838358
Category: Mathematics
Page: 352
View: 5484
In the early twentieth century, Hausdorff developed an axiomatic approach to topology, which continues to be the foundation of modern topology. The present book, the English translation of the third edition of Hausdorff's Mengenlehre, is a thorough introduction to his theory of point-set topology. The treatment begins with topics in the foundations of mathematics, including the basics of abstract set theory, sums and products of sets, cardinal and ordinal numbers, and Hausdorff's well-ordering theorem. The exposition then specializes to point sets, where major topics such as Borel systems, first and second category, and connectedness are considered in detail. Next, mappings between spaces are introduced. This leads naturally to a discussion of topological spaces and continuous mappings between them. Finally, the theory is applied to the study of real functions and their properties. The book does not presuppose any mathematical knowledge beyond calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first-year graduate students should have no difficulty in making the material their own.

Metric Spaces

Including Fixed Point Theory and Set-valued Maps
Author: Qamrul Hasan Ansari
Publisher: Alpha Science International Limited
ISBN: 9781842656556
Category: Science
Page: 196
View: 3580
METRIC SPACES is intended for undergraduate students offering a course of metric spaces and post graduate students offering a course of nonlinear analysis or fixed point theory. The first six chapters cover basic concepts of metric spaces, separable spaces, compact spaces, connected spaces and continuity of functions defined on a metric space. Chapter seven is devoted to the metric fixed point theory. Banach contraction theorem and several of its generalizations along with their applications and Caristi's fixed point theorem are also given in this chapter. The introductory set-valued analysis with special emphysis on continuity and fixed point theory of set-valued maps is given in chapter eight. One of the most useful and important results from nonlinear analysis is Ekeland's variational principle. This principle along with several of its equivalent forms, Takahashi's minimization theorem, introduction of theory of equilibrium problems and the equilibrium version of Ekeland's variational principle and several of its equivalent forms are presented in the last chapter. This book will also be useful for researchers working in nonlinear analysis, optimization and theory of equilibrium problems.

Metric Spaces

Iteration and Application
Author: Victor Bryant
Publisher: Cambridge University Press
ISBN: 9780521318976
Category: Mathematics
Page: 104
View: 2273
An introduction to metric spaces for those interested in the applications as well as theory.

Metric Spaces

Author: E. T. Copson
Publisher: CUP Archive
ISBN: 9780521357326
Category: Mathematics
Page: 152
View: 9670
Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.