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 RNS,CNS st X c= dom f & f|X is constant holds f
  is_uniformly_continuous_on X by Th27,NCFCONT1:114;
