:: deftheorem defines is_continuous_on NCFCONT1:def 16 :
for RNS being RealNormSpace
for f being PartFunc of the carrier of RNS,COMPLEX
for X being set holds
( f is_continuous_on X iff ( X c= dom f & ( for x0 being Point of RNS st x0 in X holds
f | X is_continuous_in x0 ) ) );