:: deftheorem defines is_continuous_on NFCONT_1:def 7 :
for S, T being RealNormSpace
for f being PartFunc of S,T
for X being set holds
( f is_continuous_on X iff ( X c= dom f & ( for x0 being Point of S st x0 in X holds
f | X is_continuous_in x0 ) ) );