:: deftheorem defines is_continuous_in NCFCONT1:def 7 :
for RNS being RealNormSpace
for CNS being ComplexNormSpace
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 seq being sequence of RNS st rng seq c= dom f & seq is convergent & lim seq = x0 holds
( f /* seq is convergent & f /. x0 = lim (f /* seq) ) ) ) );