Hausdorff Approximations (Mathematics and its Applications, 50)

'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point a1Ie.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series Front Matter....Pages i-xix Elements of Segment Analysis....Pages 1-22 Hausdorff Distance....Pages 23-48 Linear Methods of Approximation....Pages 49-107 Best Hausdorff Approximations....Pages 108-226 Converse Theorems....Pages 227-262 ε-Entropy, ε-Capacity and Widths....Pages 263-303 Approximation of Curves and Compact Sets in the Plane....Pages 304-321 Numerical Methods of best Hausdorff Approximation....Pages 322-331 Back Matter....Pages 333-364