  The study of low regularity (in-)extendibility of Lorentzian manifolds is
motivated by the question whether a given solution to the Einstein equations
can be extended (or is maximal) as a weak solution. In this paper we show that
a timelike complete and globally hyperbolic Lorentzian manifold is
$C^0$-inextendible. For the proof we make use of the result, recently
established by S\"amann [17], that even for \emph{continuous} Lorentzian
manifolds that are globally hyperbolic, there exists a length-maximizing causal
curve between any two causally related points.
