reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace;

theorem Th45:
  for x being Point of X st Cl {x} = {x} holds {x} is maximal_anti-discrete
proof
  let x be Point of X;
  assume
A1: Cl {x} = {x};
  {x} is anti-discrete by Th6;
  hence thesis by A1,Th17;
end;
