Semigroup compactifications of automorphism groups of ultrahomogeneous cyclically ordered sets

For the automorphism group of an ultrahomogeneous cyclically ordered set (with permutation topology) we describe three proper Ellis semigroup compactifications and compare them with the Roelcke compactification. We show that the group G of transformations of a discrete space (with permutation topology) has a semitopological semigroup compactification, and we present an initial description of the Roelcke uniformity on G. Bibliography: 27 titles.