On convergent sequences in the Stone space of one Boolean algebra

We consider the Stone space of the Boolean algebra, constructed by M.G. Bell (see Example 2.1 in [2]), which is the compactification, BN, of the countable discrete space N  . Here we consider convergent sequences in BN∖NBN∖N.We prove that if a point x∈BN∖Nx∈BN∖N is the limit of some sequence {sn:n∈ω}{sn:n∈ω} from N  , or a point x∈[A]∖Ax∈[A]∖A, where A⊆NA⊆N is a strict anti-chain in N  , then there is a sequence in BN∖NBN∖N, that converges to x.We also prove that if A is a countable discrete set of u  -points in BN∖NBN∖N and x∈[A]∖Ax∈[A]∖A, then x   is not the limit of any sequence of points of BN∖NBN∖N.