Let H be the space of real sequences x = $(x_1 , x_2, ... )$ with $\sum(x_n^2)$ finite. (This is $l_2$ in fact.) I wish to show the following:
The topology on H is different from the topology it would inherit as a subspace of R (the reals) raised to the power of aleph-null, $\aleph_0$.
Anything with this regard will definitely help, as I am not sure how to begin.
Thanks.