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Continuity Theory

Authors: Nel, Louis

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  • Approaches the topic of continuity theory with a self-contained approach accessible to students
  • Enriches the study of continuity theory by expanding its context beyond metric spaces and topological theory, into power spaces
  • Formalizes results which had previously appeared only in research-oriented publications
  • Includes a systematic study of linear continuity, providing a foundation for a deeper understanding of functional analysis
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-31159-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-3-319-31158-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-80978-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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

Reviews

“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 Künzi, zbMATH 1350.54001, 2017)


Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-31159-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-3-319-31158-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-80978-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Continuity Theory
Authors
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-31159-3
DOI
10.1007/978-3-319-31159-3
Hardcover ISBN
978-3-319-31158-6
Softcover ISBN
978-3-319-80978-6
Edition Number
1
Number of Pages
XIX, 460
Number of Illustrations
110 b/w illustrations
Topics