Alexandrov topology

English Etymology Along with the closely related concept of en Alexandrov-discrete space, after Russian mathematician Pavel Sergeyevich Alexandrov. Noun en topology A topology in which the intersection of any family of open sets is an open set. en 1972 w:Roger Penrose Techniques of Differential Topology in Relativity Society for Industrial and Applied Mathematics SIAM https://books.google.com.au/books?id=H-Mw5y0HwzUC&pg=PA34&dq=%22Alexandrov+topology%22%7C%22Alexandrov+topologies%22&hl=en&sa=X&ved=0ahUKEwiA9rnAmOfbAhXII5QKHY6ZDGYQ6AEIRDAF#v=onepage&q=%22Alexandrov%20topology%22%7C%22Alexandrov%20topologies%22&f=false 34 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. en 1990 Palle Yourgrau Demonstratives https://books.google.com.au/books?id=--zWAAAAMAAJ&q=%22Alexandrov+topology%22%7C%22Alexandrov+topologies%22&dq=%22Alexandrov+topology%22%7C%22Alexandrov+topologies%22&hl=en&sa=X&ved=0ahUKEwiA9rnAmOfbAhXII5QKHY6ZDGYQ6AEIuQEwGQ 252 w:Oxford University Press 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. 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, LNCS 10020, page 134, (6) is the family of open sets of the Alexandrov topology induced by and is the family of closed sets of the Alexandrov topology induced by ; 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. en eponyms