:: deftheorem defines T_0TSP_1:def 3 : for T being TopStruct holds ( T is T_0 iff ( T is empty or for x, y being Point of T holds ( not x <> y or ex V being Subset of T st ( V is open & x in V & not y in V ) or ex W being Subset of T st ( W is open & not x in W & y in W ) ) ) );