Geodesic
Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 42-50

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.
DOI : 10.4153/CMB-2012-027-7
Mots-clés : 46B20, 46C05, 52C17, point finite coverings, slices, polyhedral spaces, Hilbert spaces 
Fonf, Vladimir P.; Zanco, Clemente. Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 42-50. doi: 10.4153/CMB-2012-027-7
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