reserve x,X,X2,Y,Y2 for set;
reserve GX for non empty TopSpace;
reserve A2,B2 for Subset of GX;
reserve B for Subset of GX;

theorem Th11:
  for V being Subset of GX st V is connected & V<>{} holds
  Component_of (Component_of V)=Component_of V
proof
  let V be Subset of GX;
  assume V is connected & V<>{};
  then Component_of V is a_component by Th8;
  hence thesis by Th7;
end;
