Ultrafilter semigroups generated by direct sums

Let λ be an infinite cardinal and for every ordinal α<λ, let A _α be a set with a distinguished element 0 _α ∈A _α . The direct sum of sets A _α , α<λ, is the subset \(X=\bigoplus_{\alpha<\lambda}A_{\alpha}\) of the Cartesian product ∏_α<λ A _α consisting of all x with finite supp?(x)={α<λ:x(α)≠0 _α }. Endow X with a topology by taking as a neighborhood base at x∈X the subsets of the form {y∈X:y(α)=x(α) for all α<γ} where γ<λ. Let Ult?(X) denote the set of all nonprincipal ultrafilters on X converging to 0∈X. There is a natural partial semigroup operation on X which induces a semigroup operation on Ult?(X). We show that if direct sums X and Y are homeomorphic, then the semigroups Ult?(X) and Ult?(Y) are isomorphic.