The category RoTop of topological Ro-spaces and continuous maps can be embedded as a nice subcategory into Near, the category of nearness spaces and nearness preserving maps. The resulting subcategory TNear of Near has the property that products and subspaces of TNear-objects taken in Near are generally different from those taken in TNear. This led H.Herrlich — who introduced nearness spaces — to the problem to characterize those spaces belonging to the epireflective hull EH(TNear) of TNear in Near internally, which is still open.