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.
Covering the unit sphere of certain Banach spaces by sequences of slices and balls / V. P. Fonf, C. Zanco. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 0008-4395. - 57 (2014):1(2012 Sep 21), pp. 42-50. [10.4153/CMB-2012-027-7]
Covering the unit sphere of certain Banach spaces by sequences of slices and balls
C. ZancoUltimo
2012
Abstract
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
