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 .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.
@article{10_4153_CMB_1968_080_1,
author = {Oler, N.},
title = {Elements of {Packing} and {Covering}},
journal = {Canadian mathematical bulletin},
pages = {671--677},
year = {1968},
volume = {11},
number = {5},
doi = {10.4153/CMB-1968-080-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-080-1/}
}
TY - JOUR
AU - Oler, N.
TI - Elements of Packing and Covering
JO - Canadian mathematical bulletin
PY - 1968
SP - 671
EP - 677
VL - 11
IS - 5
UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-080-1/
DO - 10.4153/CMB-1968-080-1
ID - 10_4153_CMB_1968_080_1
ER -
%0 Journal Article
%A Oler, N.
%T Elements of Packing and Covering
%J Canadian mathematical bulletin
%D 1968
%P 671-677
%V 11
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-080-1/
%R 10.4153/CMB-1968-080-1
%F 10_4153_CMB_1968_080_1
