Geodesic
On Covering the Unit Ball in Normed Spaces
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 107-109

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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. 
Connett, J. On Covering the Unit Ball in Normed Spaces. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 107-109. doi: 10.4153/CMB-1971-019-9
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