 Ellentuck Borel sets are completely Ramsey

Every Borel set for the Ellentuck topology is completely Ramsey. First, an acceptance-and-rejection fusion makes every open set homogeneous after thinning the infinite reservoir while keeping its finite stem. Every nowhere-dense set is consequently completely Ramsey-null, and a fusion handling all subsets of each finite selected prefix shows that countable unions of such null sets remain null. Finally, sets differing from an open set by a meagre set form a sigma-algebra containing the open sets. Thus every Borel set has the required stem-preserving homogeneous refinement.