theorem Th21: :: TIETZE_2:21

for T being TopSpace
for n being non zero Nat
for F being Element of n -tuples_on (Funcs ( the carrier of T, the carrier of R^1)) st ( for i being Nat st i in dom F holds
for h being Function of T,R^1 st h = F . i holds
h is continuous ) holds
<:F:> is continuous