On the Closure of the Product and Sum of Linear Relations

In this paper we give two topological conditions on the graphs of two linear relations E and F on a Hilbert space ${\mathcal H}$ , one of which is sufficient to ensure the closure of the product EF, the other being sufficient to ensure the closure of the sum E?+?F. Note that these conditions are not necessary and in particular do not include the cases when E and F are continuous everywhere defined operators. Other related results are established.