These restatements help to explain why one speaks of a "specialization": "y" is more general than "x", since it is contained in more open sets. This is particularly intuitive if one views closed sets as properties that a point "x" may or may not have. The more closed sets contain a point, the more properties the point has, and the more special it is. The usage is consistent with the classical logical notions of genus and species; and also with the traditional use of generic points in algebraic geometry, in which closed points are the most specific, while a generic point of a space is one contained in every nonempty open subset. Specialization as an idea is applied also in valuation theory.