:: deftheorem defines is_continuous_on NCFCONT1:def 15 :
for CNS being ComplexNormSpace
for f being PartFunc of the carrier of CNS,REAL
for X being set holds
( f is_continuous_on X iff ( X c= dom f & ( for x0 being Point of CNS st x0 in X holds
f | X is_continuous_in x0 ) ) );