reserve T for TopSpace,
  A, B for Subset of T;

theorem :: Theorem 3
  A is regular_closed iff A is subcondensed & A is closed
proof
  thus A is regular_closed implies A is subcondensed & A is closed
  proof
    assume A is regular_closed;
    then
A1: Cl Int A = A by TOPS_1:def 7;
    thus thesis by A1;
  end;
  assume that
A2: A is subcondensed and
A3: A is closed;
  Cl Int A = Cl A by A2;
  hence thesis by A3,PRE_TOPC:22;
end;
