A categorical characterization of the categoryHausof Hausdorft topological spaces within the category Top of topological spaces is given. A notion of a Hausdorff nearness space is then introduced and it is proved that the resulting subcategoryHaus Nearof the categoryNearof nearness spaces fulfills exactly the same characterization as derived forHausinTop.Properties ofHaus Nearand relations to other important sub-categories ofNearare studied.