i got this question maybe one of you could help :
$X = [0,1] \ ^ { \Bbb N}$ , is there a metric on $X$ that induce the box topology?
i think no, i defined $A=(0,1] \ ^{\Bbb N}$ , so $\overline A = X$ , and i want to show that there is an element of $\overline A$ that there is no sequence of elements from $A$ that convergences to that element in contradiction to the fact that $X$ is metrizable.
I thought taking $(0,1,0,1\dots$ but i see now that it is incorrect. someone see another element that would work?