reserve X,X1 for set,
  r,s for Real,
  z for Complex,
  RNS for RealNormSpace,
  CNS, CNS1,CNS2 for ComplexNormSpace;

theorem
  for f be PartFunc of CNS,RNS, Y be Subset of CNS st Y c= dom f & Y is
compact & f is_uniformly_continuous_on Y holds f.:Y is compact by Th20,
