Given the metric space (M,d) where M = RxR and d(x,y) = the Euclidean metric, what is the interior of the subset of M, QxQ?
I realize it is the empty set because there are points that lie in the open ball of any element of QxQ that are not actually in the set QxQ.
What I am struggling with is giving a formal, reasonable justification of why the interior is the empty set.
Any help or suggestions to get me thinking in a good direction would be greatly appreciated. Thank you so much, in advance!
Note: The product topology coincides with the usual topology on