theorem Th49: :: C0SP3:49

for S being non empty TopSpace
for T being NormedLinearTopSpace
for H being Functional_Sequence of the carrier of S, the carrier of T
for LimH being Function of S,T st H is_unif_conv_on the carrier of S & ( for n being Nat ex Hn being Function of S,T st
( Hn = H . n & Hn is continuous ) ) & LimH = lim (H, the carrier of S) holds
LimH is continuous