:: deftheorem defines is_continuous_in NCFCONT1:def 5 :
for CNS1, CNS2 being ComplexNormSpace
for f being PartFunc of CNS1,CNS2
for x0 being Point of CNS1 holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for seq being sequence of CNS1 st rng seq c= dom f & seq is convergent & lim seq = x0 holds
( f /* seq is convergent & f /. x0 = lim (f /* seq) ) ) ) );