Topology of event horizons

The topology of event horizons is investigated. Considering the existence of the end point of the event horizon, the event horizon cannot be differentiable. Then there are new possibilities for the topology of the event horizon, excluded in smooth event horizons. The relation between the spatial topology of the event horizon and its end points is revealed. A toroidal event horizon is caused by two-dimensional end point sets. One-dimensional end point sets provide the coalescence of spherical event horizons. Moreover, these aspects can be removed by an appropriate time slicing. The result will be useful to discuss the stability and generality of the topology of the event horizon.