theorem Th33:
  for S, T be RealNormSpace,
      I be LinearOperator of S,T,
      Z be Subset of S
    st I is one-to-one onto isometric-like
  holds I is_continuous_on Z
  proof
    let S, T be RealNormSpace;
    let I be LinearOperator of S,T,
    Z be Subset of S;
    assume
    A1: I is one-to-one onto isometric-like;
    A2: dom I = the carrier of S by FUNCT_2:def 1;
    for x be Point of S st x in dom I holds
    I | (dom I) is_continuous_in x by A1,Th32;
    hence thesis by A2,NFCONT_1:23,NFCONT_1:def 7;
  end;
