
theorem Th38:
  for V being RealUnitarySpace holds the carrier of V in Family_open_set(V)
proof
  let V be RealUnitarySpace;
  the carrier of V c= the carrier of V & for v being Point of V st v in
  the carrier of V
    ex p being Real st p>0 & Ball(v,p) c= the carrier of V
  by Th34;
  hence thesis by Def5;
end;
