# Search Results for "elements-of-metric-spaces"

## Elements of Metric Spaces

**Author**: N.A**Publisher:**Academic Publishers**ISBN:**9788189781989**Category:**Metric spaces**Page:**204**View:**3550

## Metric Spaces

**Author**: Mícheál O'Searcoid**Publisher:**Springer Science & Business Media**ISBN:**9781846286278**Category:**Mathematics**Page:**304**View:**3774

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 General Topology

**Author**: K. D. Joshi**Publisher:**New Age International**ISBN:**9780852264447**Category:**Topology**Page:**412**View:**9427

## Metric Space

**Author**: S.C. Sharma**Publisher:**Discovery Publishing House**ISBN:**9788183561181**Category:**Metric spaces**Page:**300**View:**4443

This book Metric Space has been written for the students of various universities. In the earlier chapters, proof are given in considerable detail, as our subject unfolds through the successive chapters and the reader acquires experience in following abstract mathematical arguments, the proof become briefer and minor details are more and more left for the reader to fill in for himself. It is a basic principle in the study of mathematics, and one too seldom emphasised that a proof is not really understood until the stage is reached at which one can grasp it is a whole and see it as a single idea. In achieving this end much more is necessary than merely following the individual steps in the reasoning. Contents: Basic Concept of Set, Metric Space, Compactness.

## Elements of the Theory of Functions and Functional Analysis

**Author**: Andre? Nikolaevich Kolmogorov,Serge? Vasil?evich Fomin,S. V. Fomin**Publisher:**Courier Corporation**ISBN:**9780486406831**Category:**Mathematics**Page:**288**View:**6604

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

## Foundations of Modern Analysis

**Author**: Avner Friedman**Publisher:**Courier Corporation**ISBN:**9780486640624**Category:**Mathematics**Page:**250**View:**3455

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

## Fundamentals of Signal Processing in Metric Spaces with Lattice Properties

*Algebraic Approach*

**Author**: Andrey Popoff**Publisher:**CRC Press**ISBN:**1351597124**Category:**Mathematics**Page:**418**View:**9990

Exploring the interrelation between information theory and signal processing theory, the book contains a new algebraic approach to signal processing theory. Readers will learn this new approach to constructing the unified mathematical fundamentals of both information theory and signal processing theory in addition to new methods of evaluating quality indices of signal processing. The book discusses the methodology of synthesis and analysis of signal processing algorithms providing qualitative increase of signal processing efficiency under parametric and nonparametric prior uncertainty conditions. Examples are included throughout the book to further emphasize new material.

## Elements of Point Set Topology

**Author**: John D. Baum**Publisher:**Courier Corporation**ISBN:**0486668266**Category:**Mathematics**Page:**150**View:**9007

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

## Lectures and Exercises on Functional Analysis

**Author**: Александр Яковлевич Хелемский**Publisher:**American Mathematical Soc.**ISBN:**9780821889695**Category:**Mathematics**Page:**468**View:**5299

The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.

## Elements of Functional Analysis

**Author**: I. J. Maddox**Publisher:**CUP Archive**ISBN:**9780521358682**Category:**Mathematics**Page:**242**View:**2286

This 1970 textbook aims to provide a truly introductory course in functional analysis.