In 1975, it was proven that a space is  iff its -identification space is Hausdorff. The 1975 work motivated the introduction and investigation of weakly Po properties, which led to the introduction and investigation of weakly P1, weakly P2, and weakly  properties. Within the recent papers, it was established that in weakly P1 spaces  and  are equivalent, in weakly P2 spaces  and  are equivalent, and in weakly  spaces  and Urysohn are equivalent. Within this paper weakly  is further investigated with infinitely many topological properties, in addition to weakly  given for each weakly  for which each of  and Urysohn are equivalent and results in this paper are used to give infinitely many new characterizations of the Urysohn separation axiom.

topological properties, weakly P properties, Urysohn.