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Introduction: The Problem to be Solved Read chapter Read first chapter

2013 | OriginalPaper | Chapter

2. Basic Fundamentals: What You Need to Know

Author : Volker Michel

Published in: Lectures on Constructive Approximation

Publisher: Birkhäuser Boston

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Abstract

If you want to learn how to cook the perfect soufflé, you first have to know how to beat egg white. It is not easy but easier than cooking the whole soufflé. However, if your beaten egg white does not have the right consistency, your soufflé won’t become satisfactory.

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previous chapter Introduction: The Problem to be Solved
next chapter Approximation of Functions on the Real Line
Footnotes
1
Nonmathematicians might want to ignore this problem and the following considerations of part (2) and just accept that there is a particular difference between \({\mathcal{L}}^{p}\) and \({\mathrm{L}}^{p}\). The rest of this book will, nevertheless, be comprehensible.
 
2
Actually, this is a particular case of a more general concept on normed spaces.
 
3
More precisely, this is the concept of a closed set in the topology. Later, we will also get to know the concept of a closed set in the sense of the approximation theory.
 
4
If X is complete, it suffices to know that Y is closed.
 
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Metadata
Title
Basic Fundamentals: What You Need to Know
Author
Volker Michel
Copyright Year
2013
Publisher
Birkhäuser Boston
Book
Lectures on Constructive Approximation

Print ISBN: 978-0-8176-8402-0

Electronic ISBN: 978-0-8176-8403-7

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-0-8176-8403-7_2

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