Intersections of Centred Sets in Normed Spaces


Various kinds of closed centred sets in normed spaces are considered. Necessary and sufficient conditions are obtained for every decreasing sequence of such sets to have nonempty intersection. Let X be a real or complex normed space. Recall that a set S ⊆ X is symmetric if S = −S and balanced if tS ⊆ S for all t ∈ [−1, 1]. It is convenient to introduce the… (More)