theorem Th8: :: NFCONT_3:8

for x0 being Real
for S being RealNormSpace
for f being PartFunc of REAL, the carrier of S holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for r being Real st 0 < r holds
ex s being Real st
( 0 < s & ( for x1 being Real st x1 in dom f & |.(x1 - x0).| < s holds
||.((f /. x1) - (f /. x0)).|| < r ) ) ) ) )