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Elements of Packing and Covering
Published online by Cambridge University Press: 20 November 2018
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The term 'covering' is known to any student who has seen the Heine-Borel theorem and he soon learns that it denotes a very basic and widely used concept. Quite generally, a family {Xα: α ∈ A} of a subsets of X is a covering of the subset Y of X if 
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The concept of packing is perhaps no less frequently encountered although the term has only a rather specialized use. In general, a packing is any family of subsets {Xα: α ∈ A} of a set X which a re pairwise disjoint. To make this definition more similar to that of covering, we might define {Xα} to be a packing of the subset Y of X if Xα ∩ Xβ ∩ Y = ϕ for α ≠ β. This is intended to suggest only a P that there is a certain parallel between the ideas of packing and covering but not a duality in any technical sense.
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- Research Article
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- Copyright © Canadian Mathematical Society 1968
References
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Macbeath, A.M., Abstract theory of packings and coverings I. Proc. Glasgow Math. Assoc. 4 (1959) 92-95.Google Scholar
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Fejes-Toth, L., Lagerungen in der Ebene auf der Kugel und im Raum. (Springer, Berlin, 1953).Google Scholar
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Cassels, J. W.S., An introduction to the geometry of numbers. (Springer, Berlin, 1959).Google Scholar
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