Continuity Theory

Author:   Louis Nel
Publisher:   Springer International Publishing AG
Edition:   1st ed. 2016
ISBN:  

9783319311586


Pages:   460
Publication Date:   14 June 2016
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Continuity Theory


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Overview

This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject's classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, especially those that contribute to a better understanding of functional analysis, towards establishing an efficient setting for its pursuit.

Full Product Details

Author:   Louis Nel
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2016
Dimensions:   Width: 15.50cm , Height: 3.00cm , Length: 23.50cm
Weight:   9.264kg
ISBN:  

9783319311586


ISBN 10:   3319311581
Pages:   460
Publication Date:   14 June 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Overview.- General Preparation.- Continuity Enabling Structures.- Construction of New Spaces.- Various Kinds of Spaces.- Fundamentals of Linear Continuity.- Basic Categorical Concepts.- The Category C.- Reflective Categories of C.- Enriched Dualities.- The Category CV.- Reflective Subcategories of CV.- Linear Continuous Representations.- Smooth Continuity.- Supplementary Reading.

Reviews

The author presents the theory of continuous mappings, mainly in the realm of convergence spaces ... . contains many exercises and a section on supplementary reading. The work is addressed to readers who have studied continuous mappings in the metric setting, as well as multidimensional differential calculus. ... book will mainly be studied and used by mature readers and lecturers, who will appreciate the wealth of information that it provides, much of which is not available in book form elsewhere. (Hans Peter Kunzi, zbMATH 1350.54001, 2017)


This book is devoted to the so-called continuity theory, which includes continuous mappings between topological, metric and convergence spaces. Primarily, the book is designed for students, but it also contains some information which could be interesting for advanced readers. ... In conclusion, the book contains very interesting and somewhat unusual treatments of continuity. (Vesko Valov, Mathematical Reviews, August, 2017) The author presents the theory of continuous mappings, mainly in the realm of convergence spaces ... . contains many exercises and a section on supplementary reading. The work is addressed to readers who have studied continuous mappings in the metric setting, as well as multidimensional differential calculus. ... book will mainly be studied and used by mature readers and lecturers, who will appreciate the wealth of information that it provides, much of which is not available in book form elsewhere. (Hans Peter Kunzi, zbMATH 1350.54001, 2017)


Author Information

Louis D. Nel is Professor Emeritus of Mathematics at Carleton University. His research interests include topology, category theory, and functional analysis.

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