Two spaces homeomorphic to Seq ( p )

We consider the spaces called Seq(ut), constructed on the set Seq of all finite sequences of natural numbers using ultrafilters ut to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that S(ut) is homogeneous if and only if all the ultrafilters ut have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to Seq(p) (i.e., ut = p for all t ∈ Seq). It follows that for a Ramsey ultrafilter p, Seq(p) is a topological group.