Alexandrov topology

Etymology
Along with the closely related concept of, after Russian mathematician.

Noun

 * 1)  A topology in which the intersection of any family of open sets is an open set.
 * 2) * 2016, Piero Pagliani, Covering Rough Sets and Formal Topology — A Uniform Approach Through Intensional and Extensional Operators, James F. Peters, Andrzej Skowron (editors), Transactions on Rough Sets XX, Springer, 10020, page 134,
 * (6) $$S_{0,2}(P(R_C))$$ is the family of open sets of the Alexandrov topology induced by $$R_C$$ and $$S^{0,5,7}(P(R_C))$$ is the family of closed sets of the Alexandrov topology induced by $$R^{\smile}_C$$;
 * 1) * 2016, Piero Pagliani, Covering Rough Sets and Formal Topology — A Uniform Approach Through Intensional and Extensional Operators, James F. Peters, Andrzej Skowron (editors), Transactions on Rough Sets XX, Springer, 10020, page 134,
 * (6) $$S_{0,2}(P(R_C))$$ is the family of open sets of the Alexandrov topology induced by $$R_C$$ and $$S^{0,5,7}(P(R_C))$$ is the family of closed sets of the Alexandrov topology induced by $$R^{\smile}_C$$;

Usage notes
By the axioms of topology, the intersection of any finite family of open sets is open; in Alexandrov topologies the same is true for infinite families.