:: deftheorem defines is_continuous_in NFCONT_3:def 1 :
for S being RealNormSpace
for f being PartFunc of REAL, the carrier of S
for x0 being Real holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for s1 being Real_Sequence st rng s1 c= dom f & s1 is convergent & lim s1 = x0 holds
( f /* s1 is convergent & f /. x0 = lim (f /* s1) ) ) ) );