Let and
a sequence such that
Prove that f is continuos in
if and only if
converges to zero
thanks!
Careful there, this is only an if and only if theorem if X is metrizable.
In general it is only true that a function being continuous implies for every convergent sequence implies .
Obviously is metrizable, so it is okay to use here, but just want to make sure no passerby thinks this theorem is true in general as you have it stated