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Continuity Theory

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概要 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 mult...idimensional 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.続きを見る
目次 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. .
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2016 English/International

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登録日 2020.06.27
更新日 2020.06.28