Let \(C(H)\) denotes the set of closed linear operators in a Hilbert space \(H\). If \(A, B\in C(H)\), then \(AB\) need not be closed. In fact, the product of a closed symmetric operator \(A\) with itself may have a domain that reduces to \(\{0\}\). An important property is that if \(A\) and \(B\) in \(C(H)\) are close to each other with respect to the gap metric, then their product remains in \(C(H)\) [J.Ph.Labrousse, Rend.Circ.Mat.Palermo 29, 161–258 (1980; Zbl 0474.47008)]. The authors show that if the distance between two closed operators with respect to some metric in \(C(H)\) is fairly small, then their usual product is closed.