  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.
