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

Let {f_n} be a sequence of functions from

f_n (s)=1/n if 1<=s<=n

f_n (s)=0 if s>n.

Define f:

a) Does {f_n} (n=1 to inf) converge to f in the

b) when endowed with the box topology?

Thanks again.

Let {f_n} be a sequence of functions from

**N**(set of natural numbers) to**R**(real nos.) wheref_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.

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