for CNS being ComplexNormSpace
for RNS being RealNormSpace
for f being PartFunc of RNS,CNS
for x0 being Point of RNS holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for N1 being Neighbourhood of f /. x0 ex N being Neighbourhood of x0 st
for x1 being Point of RNS st x1 in dom f & x1 in N holds
f /. x1 in N1 ) ) )