Chains of controllable partitions of the m-dimensional cube

Preprint series: 99-40, Reports on Analysis

The paper is published: Arch. Math. 68 (1997), 331-339

MSC:
52C07 Lattices and convex bodies in \$n\$ dimensions, See Also {11H06, 11H31, 11P21}
41A30 Approximation by other special function classes

Abstract: Controllable partitions, which arise in approximation theory,
are finite partitions of compact metric spaces into subsets
whose sizes fulfil a uniformity condition depending on the
entropy numbers of the underlying space. We characterize a
class of partitions of the cube \$([0,2]^m,d_\max)\$ which
possess a controllable refinement and, in the end, give an
ascending chain of controllable partitions of \$[0,2]^m\$.

Keywords: cube, finite partition, entropy number, refinement of a partition, chain of partitions