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On the dimensions of ordered sets of bounded degree

✍ Scribed by Z. Füredi; J. Kahn

Publisher
Springer Netherlands
Year
1986
Tongue
English
Weight
289 KB
Volume
3
Category
Article
ISSN
0167-8094

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✦ Synopsis

Here it is proven that there exists a constant c (c < 50) such that dim P < ck(log k) *. This improves an earlier result of Rod1 and Trotter (dim P < 2k' + 2). Our proof is nonconstructive, depending in part on LOW&Z local lemma. AMS (MOS) subject classification (1980). 06AlO.

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The degree of approximation of infinite-dimensional function classes using finite n-dimensional manifolds has been the subject of a classical field of study in the area of mathematical approximation theory. In Ratsaby and Maiorov (1997), a new quantity p,(F, L,) which measures the degree of approxim