reserve r for Real;
reserve a, b for Real;
reserve T for non empty TopSpace;
reserve A for non empty SubSpace of T;
reserve P,Q for Subset of T,
  p for Point of T;
reserve M for non empty MetrSpace,
  p for Point of M;
reserve A for non empty SubSpace of M;

theorem Th8:
  for p being Point of A holds p is Point of M
proof
  let p be Point of A;
  p in the carrier of A & the carrier of A c= the carrier of M by Def1;
  hence thesis;
end;
