reserve Y for TopStruct;
reserve X for non empty TopSpace;
reserve X for almost_discrete non empty TopSpace;
reserve X,Y for non empty TopSpace;
reserve X for discrete non empty TopSpace,
  X0 for non empty SubSpace of X;
reserve X for almost_discrete non empty TopSpace,
  X0 for maximal_discrete non empty SubSpace of X;

theorem
  for r being continuous Function of X,X0 holds r is being_a_retraction
implies for a being Point of X0, b being Point of X st a = b holds r" {a} = Cl
  {b} by Th70;
