  Separation systems are posets with additional structure that form an abstract
setting in which tangle-like clusters in graphs, matroids and other
combinatorial structures can be expressed and studied.
  This paper offers some basic theory about infinite separation systems and how
they relate to the finite separation systems they induce. They can be used to
prove tangle-type duality theorems for infinite graphs and matroids, which will
be done in future work that will build on this paper.
