theorem Th24: :: NFCONT_4:24

for n being Element of NAT
for X being set
for f being PartFunc of REAL,(REAL n) st X c= dom f holds
( f | X is continuous iff for x0, r being Real st x0 in X & 0 < r holds
ex s being Real st
( 0 < s & ( for x1 being Real st x1 in X & |.(x1 - x0).| < s holds
|.((f /. x1) - (f /. x0)).| < r ) ) )