Topological Censorship in Spacetimes Compatible with $$\Lambda > 0$$

Currently available topological censorship theorems are meant for gravitationally isolated black hole spacetimes with cosmological constant $$\Lambda =0$$ or <0$$ . Here, we prove a theorem that is compatible >0$$ and which can be applied to whole universes containing possibly multiple collections of holes. The main assumption in the distinct eventually become from one another at late times, conclusion regions near various have trivial fundamental group, spite there being nontrivial topology universe.