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Erschienen in:
2013 | OriginalPaper | Buchkapitel
2. Functions and Relations
verfasst von : Li M. Chen
Erschienen in: Digital Functions and Data Reconstruction
Verlag: Springer New York
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Abstract
This chapter overviews the basic concepts of functions and relations including continuous functions and their differentiations in Euclidean space. We also introduce functions in discrete spaces, specifically graphs and grid spaces. This chapter contains three parts: continuous functions in Euclidean space, graphs and discrete spaces, and advanced topics including topological spaces. Philosophically, a space is a relation or a collection of relations over a set. A graph is a relation; an m-dimensional Euclidean Space is a collection of relations over points in R
m
. This chapter is written in a gradual progression to provide a simple and interesting review of the background knowledge. Some of the more profound issues will be presented in later chapters as needed. Those with a strong background in mathematics can skip some or all of this chapter. This chapter prepares the necessary basic knowledge for the rest of the book.