On the Geroch-Kronheimer-Penrose future completion \(IP(X)\) of a spacetime X, there are two frequently used topologies. We systematically examine \(\tau _+\) , the stronger (metrizable) of them, which is the coarsest causally continuous topology, obtaining a variety of novel results, among them a complete characterization of the difference in convergence between both topologies. In our framework, we can allow for X being a chr. space and consequently for the interpretation of IP as an idempotent functor on a category that includes spacetimes of very low regularity. Furthermore, we explicitly calculate \((IP(X), \tau _+)\) for multiply-warped chronological spaces.