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