reserve T,U for non empty TopSpace;
reserve t for Point of T;
reserve n for Nat;
reserve T for TopStruct;
reserve f for PartFunc of R^1, T;
reserve c for Curve of T;

theorem Th20:
  for f being parametrized-curve PartFunc of R^1, T holds f is Curve of T
  proof
    let f be parametrized-curve PartFunc of R^1, T;
    reconsider f1 = f as Element of PFuncs(REAL, [#]T)
    by PARTFUN1:45,TOPMETR:17;
    f1 in Curves T;
    hence thesis;
  end;
