theorem Th75: :: TOPGEN_5:75

for T being non empty TopSpace
for f being Function of T,I[01] holds
( f is continuous iff for a, b being Real st 0 <= a & a < 1 & 0 < b & b <= 1 holds
( f " [.0,b.[ is open & f " ].a,1.] is open ) )