Reflectionless Schrodinger operators and Marchenko parametrization

Let Tq=-d²/dx² +q be a Schr\"odinger operator in the space L₂(R). A potential q is called reflectionless if the operator Tq is reflectionless. Let Q be the set of all reflectionless potentials of the Schr\"odinger operator, and let M be the set of nonnegative Borel measures on R with compact support. As shown by Marchenko, each potential q can be associated with a unique measure μ. As a result, we get the bijection Θ Q→ M. In this paper, we show that one can define topologies on Q and M, under which the mapping Θ is a homeomorphism.