reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

theorem Th32:
  for S, T be RealNormSpace,
      I be LinearOperator of S,T,
      x be Point of S
    st I is one-to-one onto isometric-like
  holds I is_continuous_in x
  proof
    let S, T be RealNormSpace,
        I be LinearOperator of S,T,
        x be Point of S;
    assume I is one-to-one onto isometric-like;
    then I is_continuous_on the carrier of S by Th30,LOPBAN_7:6;
    hence thesis;
  end;
