reserve S,T,W,Y for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve Z for Subset of S;
reserve i,n for Nat;

theorem LM015:
  for I be LinearOperator of S,T,
      Z be Subset of S
  st I is isometric holds
    I is_continuous_on Z
  proof
    let I be LinearOperator of S,T,
    Z be Subset of S;
    assume AS: I is isometric;
    P1: 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 AS,LM010;
    hence thesis by P1,NFCONT_1:23,NFCONT_1:def 7;
  end;
