  The topologies of event horizons are investigated. Considering the existence
of the endpoint of the event horizon, it cannot be differentiable. Then there
are the new possibilities of the topology of the event horizon though they are
excluded in smooth event horizons. The relation between the topology of the
event horizon and the endpoint of it is revealed. A torus event horizon is
caused by two-dimensional endpoints. One-dimensional endpoints provide the
coalescence of spherical event horizons. Moreover, these aspects can be removed
by an appropriate timeslicing. The result will be useful to discuss the
stability and generality of the topology of the event horizon.
