If A x B = empty set then A = empty set or B = empty set.
No it does not stand for multiplication in a set theoretic context.
It is a cross product: $\displaystyle A \times B = \left\{ {\left( {a,b} \right):a \in A\,\& \,b \in B} \right\}$.
Now it is perfectly clear that if either set is empty then the cross product is empty and visa versa.