  In this thesis we propose and study a theory of ordered locales, a type of
point-free space equipped with a preorder structure on its frame of opens. It
is proved that the Stone-type duality between topological spaces and locales
lifts to a new adjunction between a certain category of ordered topological
spaces and the newly introduced category of ordered locales.
  As an application, we use these techniques to develop point-free analogues of
some common aspects from the causality theory of Lorentzian manifolds. In
particular, we show that so-called indecomposable past sets in a spacetime can
be viewed as the points of the locale of futures. This builds towards a
point-free causal boundary construction. Furthermore, we introduce a notion of
causal coverage that leads naturally to a generalised notion of Grothendieck
topology incorporating the order structure. From this naturally emerges a
localic notion of domain of dependence.
