for X being RealNormSpace
for S being sequence of X
for St being sequence of (TopSpaceNorm X)
for x being Point of X
for xt being Point of (TopSpaceNorm X) st S = St & x = xt holds
( St is_convergent_to xt iff for r being Real st 0 < r holds
ex m being Nat st
for n being Nat st m <= n holds
||.((S . n) - x).|| < r )