  In a space-time with cosmological constant $\Lambda>0$ and matter satisfying
the dominant energy condition, the area of a black or white hole cannot exceed
$4\pi/\Lambda$. This applies to event horizons where defined, i.e. in an
asymptotically deSitter space-time, and to outer trapping horizons (cf.
apparent horizons) in any space-time. The bound is attained if and only if the
horizon is identical to that of the degenerate `Schwarzschild-deSitter'
solution. This yields a topological restriction on the event horizon, namely
that components whose total area exceeds $4\pi/\Lambda$ cannot merge. We
discuss the conjectured isoperimetric inequality and implications for the
cosmic censorship conjecture.
