This textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.

arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree.

First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

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

The themes of the 1997 conference are new theoretical and practical accomplishments in logic programming, new research directions where ideas originating from logic programming can play a fundamental role, and relations between logic programming and other fields of computer science. The annual International Logic Programming Symposium, traditionally held in North America, is one of the main international conferences sponsored by the Association of Logic Programming. The themes of the 1997 conference are new theoretical and practical accomplishments in logic programming, new research directions where ideas originating from logic programming can play a fundamental role, and relations between logic programming and other fields of computer science. Topics include theoretical foundations, constraints, concurrency and parallelism, deductive databases, language design and implementation, nonmonotonic reasoning, and logic programming and the Internet.

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

The purpose of this book is to give a comprehensive introduction to the study of non-linear operator theory in probabilistic metric spaces. This book is introduced as a survey of the latest and new results on the following topics: Basic theory of probabilistic metric spaces; Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces; Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces; Coincidence point theorems, minimisation and fixed degree theorems in probabilistic metric spaces; Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces; Nonlinear semigroups and differential equations in probabilistic metric spaces; KKM theorems, minimax theorems and variational inequalities.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.