For a space X, OSM_X asserts that for any open neighbourhood assignment (or open set mapping) N, there is a partition of X into countably many pieces such that for each x, y in the same piece, either x is in N(y) or y is in N(x).

We introduce a property that will force OSM under PFA. We then use OSM to imply D, assuming additional properties (e.g., sub-Sorgenfrey).