On an example of Simon

Using the Stone spaces of subalgebras of P(N)/fin, Petr Simon constructed an extremely clever example of a compactification of N which has (1) a sequentially compact remainder and (2) no nontrivial sequence in N converges. Because of the use of Stone spaces this compactification is zero-dimensional. In this paper we provide a method of constructing examples having properties (1) and (2) while controlling other properties of the remainder. For example, the remainder may be connected.