theorem Th40: :: YELLOW_9:40

for T1, T2 being non empty TopSpace
for B1 being Basis of T1
for B2 being Basis of T2 holds { [:a,b:] where a is Subset of T1, b is Subset of T2 : ( a in B1 & b in B2 ) } is Basis of [:T1,T2:]