Timelike simply connected
Suppose a Lorentzian manifold contains a closed timelike curve. No CTC can be continuously deformed as a CTC to a point, as that point would not be causally well behaved. Therefore, any Lorentzian manifold containing a CTC is said to be timelike multiply connected. A Lorentzian manifold that does not contain a CTC is said to be timelike simply connected.
Any Lorentzian manifold which is timelike multiply connected has a diffeomorphic universal covering space which is timelike simply connected. For instance, a three-sphere with a Lorentzian metric is timelike multiply connected,, but has a diffeomorphic universal covering space which contains no CTC. By contrast, a three-sphere with the standard metric is simply connected, and is therefore its own universal cover.
