In
topology, a
coherent topology is a
topology that is uniquely determined by a family of
subspaces. Loosely speaking, a
topological space is coherent with a family of subspaces if it is a
topological union of those subspaces. It is also sometimes called the
weak topology generated by the family of subspaces, a notion which is quite different from the notion of a weak topology generated by a set of maps.