Open core and small groups in dense pairs of topological structures

Dense pairs of geometric topological fields have tame open core, that is, every definable subset in the pair is already reduct. We fix a minor gap published version van den Dries's seminal work on dense o-minimal groups, and show unary function agrees with reduct, off small subset, set internal to predicate. For certain without independence property, whenever underlying group contained dense-codense predicate, law locally reduct as field. If has elimination imaginaries, we extend this result, up interdefinability, all groups