Alexandrov topology

Noun

Alexandrov topology (plural Alexandrov topologies)

1. A topology in which the intersection of any family of open sets is an open set.
   • 4.24. THEOREM. The following three restrictions on a space-time M are equivalent:
     (a) M is strongly causal;
     (b) the Alexandrov topology agrees with the manifold topology;
     (c) the Alexandrov topology is Hausdorff.1972, Roger Penrose, Techniques of Differential Topology in Relativity, SIAM, page 34
   • In Minkowski space-time there is, indeed, a topology definable solely in terms of the causal connectivity among events, the Alexandrov topology, which is provably equivalent to the ordinary manifold topology.1990, Palle Yourgrau, Demonstratives, Oxford University Press, page 252