Some remarks on the ball-covering property

摘要: Abstract A Banach space X has the so-called ball-covering property whenever its unit sphere can be covered by a countable collection of open balls that miss origin. If 0 α 1 , then α-ball covering if those B . We show is separable and only renormed such dual ( ⦀ ⋅ ) ⁎ enjoys α-BCP for some (or all) ∈ In contrast with this, we observe separability does not always imply BCP The latter fact follows from general example: non-separable C K spaces fail in major way — they even “ − -BCP”.