Comment on “Spaces of paths and the path topology” [J. Math. Phys. 57, 092503 (2016)]

It is well known that in the study of singularity theorems, manifold topology is used to introduce topologies on collections of causal curves. A new topology is defined in [R. J. Low, J. Math. Phys. 57, 092503 (2016)] on the collection of causal curves using a physically relevant topology on Lorentz manifolds, namely the path topology, and it was derived that this topology on the collection of endless causal curves is strictly finer than the one defined with the help of manifold topology. In the present paper, it is shown that the proof of this result is incorrect when the underlying space is a two-dimensional strongly causal Lorentz manifold. A new proof is constructed which holds for all dimensions greater than or equal to two.