Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Continuity Theory
Authors: Louis Nel
DOI: https://doi.org/10.1007/978-3-319-31159-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-31158-6Published: 14 June 2016
Softcover ISBN: 978-3-319-80978-6Published: 30 May 2018
eBook ISBN: 978-3-319-31159-3Published: 03 June 2016
Edition Number: 1
Number of Pages: XIX, 460
Number of Illustrations: 110 b/w illustrations
Topics: Functional Analysis, Topology