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;
reserve x,y for Point of X;
reserve A, B for Subset of X;
reserve P, Q for Subset of X;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace,
  Y0 for non empty SubSpace of X;

theorem
  for x being Point of X st Cl {x} = {x} holds Sspace(x) is
  maximal_anti-discrete
proof
  let x be Point of X;
  assume Cl {x} = {x};
  then
A1: {x} is maximal_anti-discrete by Th45;
  the carrier of Sspace(x) = {x} by TEX_2:def 2;
  hence thesis by A1,Th72;
end;
