  Because no closed timelike curve (CTC) on a Lorentzian manifold can be
deformed to a point, any such manifold containing a CTC must have a topological
feature, to be called a timelike wormhole, that prevents the CTC from being
deformed to a point. If all wormholes have horizons, which typically seems to
be the case in space-times without exotic matter, then each CTC must transit
some timelike wormhole's horizon. Therefore, a Lorentzian manifold containing a
CTC may nevertheless be causally well behaving once its horizon's are deleted.
For instance, there may be a Cauchy-like surface through which every timelike
curve passes one and only once before crossing a horizon.
