theorem Th1: :: TOPS_4:1

for A, B, S, T being TopSpace
for f being Function of A,S
for g being Function of B,T st TopStruct(# the U1 of A, the topology of A #) = TopStruct(# the U1 of B, the topology of B #) & TopStruct(# the U1 of S, the topology of S #) = TopStruct(# the U1 of T, the topology of T #) & f = g & f is open holds
g is open