theorem
  TS is T_2 & PS is compact & QS is compact implies PS /\ QS is compact
proof
  assume that
A1: TS is T_2 and
A2: PS is compact and
A3: QS is compact;
A4: QS is closed by A1,A3,Th7;
  PS is closed by A1,A2,Th7;
  hence thesis by A2,A4,Th9,XBOOLE_1:17;
end;
