If you mean that has the "usual" metric topology on the real numbers, restricted to , and that is to be given the usual "product topology", then, yes, of course, it is a topological space. If A and B are are any two topological spaces then "with the product topology" is, by definition, a topological space. Since is not an open set in the usual topology on , no, is not an open set. Since is a closed set in the usual topology on , yes, is a closed set.