theorem Th19: :: NCFCONT1:19

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 f .: N c= N1 ) ) )