reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem Th38:
  F is dense-in-itself implies union F is dense-in-itself
proof
  assume F is dense-in-itself;
  then
A1: union F c= union Der F by Th37;
  union Der F c= Der union F by Th34;
  then union F c= Der union F by A1;
  hence thesis;
end;
