On Covering the Unit Ball in Normed Spaces

1 January 1971

journal article
Published by Canadian Mathematical Society in Canadian Mathematical Bulletin

Vol. 14 (1) , 107-109
https://doi.org/10.4153/cmb-1971-019-9

Abstract

By compactness, the unit ball Bⁿ in Rⁿ has a finite covering by translates of rBⁿ, for any r > 0. The main theorem of this note shows that a weaker covering property does not hold in any infinite-dimensional normed space.

Keywords

COMPACTNESS
UNIT BALL
HOLD
INFINITE
THEOREM
NORMED
TRANSLATES