Sousa, Lurdes2015-06-302015-06-3019960927-2852http://hdl.handle.net/10400.19/2852Each ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subcategory of alpha-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, introduced by the authour in a previous paper.engorthogonal closure operatorreflective hullalpha-sober spacejournal article