摘要：

A normed vector space has the ball-covering property if its unit sphere can be covered by countably many closed balls off the origin. Two new examples, Cb (R) and L∞ (R), are considered by introducing new but equivalent norms (| ? |a and || ? ||λ) of them. (Cb (R),| ? |a) has the ball-covering property if and only if a ∈ (1/2,1 ]. And for all λ ∈ [ 0,1 ], (L∞ (R),? λ) fails the ball-covering property.