# Math Help - convergence in the product and box topology

1. ## convergence in the product and box topology

Hi. Can I have some help in answering the following questions? Thank you.

Let {f_n} be a sequence of functions from N(set of natural numbers) to R(real nos.) where
f_n (s)=1/n if 1<=s<=n
f_n (s)=0 if s>n.
Define f:N to R by f(s)=0 for every s>=1.
a) Does {f_n} (n=1 to inf) converge to f in the R^N (cartesian product) endowed with the product topology?
b) when endowed with the box topology?

Thanks again.

2. Consider the open set (in the box topology) given by $\prod_{n=1}^\infty(-\frac1{n+1},\frac1{n+1})$.