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Hausdorff Obstructions to Packing (N-1)-Balls in N-Space

Published online by Cambridge University Press:  20 November 2018

J. B. Wilker
J. B. Wilker*
Affiliation:
University of Toronto, Toronto Ontario Canada
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Abstract

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An arbitrary collection of (N — l)-flats in ℝN is called a frame and an arbitrary assignment of (N — 1))-balls to these (N — 1)-flats is called a loading. Any loading in which the designated (N — 1)-balls are mutually disjoint is called a packing. For the frame consisting of the (N — 1)-flats perpendicular to a given line, every loading is automatically a packing. Although this is obviously not the most general frame to admit a packing, we show two senses in which all frames which admit packings are "at most onedimensional." Our principal tool is the Hausdorff measure-theoretic dimension.

Keywords

52A4528A75
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 414 - 420
Copyright
Copyright © Canadian Mathematical Society 1982

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