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