
theorem Th9:
  for PM being MetrStruct holds
  the carrier of TopSpaceMetr PM = the carrier of PM
  proof
    let PM be MetrStruct;
    the carrier of TopSpaceMetr PM=
    the carrier of TopStruct (#the carrier of PM,
    Family_open_set(PM)#) by PCOMPS_1:def 5;
    hence thesis;
  end;
