
theorem Th6:
  for T being TopSpace holds the topology of T = UniCl the topology of T
proof
  let T be TopSpace;
  thus the topology of T c= UniCl the topology of T by Th1;
  let a be object;
  assume
A1: a in UniCl the topology of T;
  then reconsider a9 = a as Subset of T;
  ex b being Subset-Family of T st b c= the topology of T & a9 = union b
  by A1,Def1;
  hence thesis by PRE_TOPC:def 1;
end;
