Meaning of Alexandrov topology | Babel Free

Definitions

A topology in which the intersection of any family of open sets is an open set.

Examples

“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.”

“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) S_0,2(P(R_C)) is the family of open sets of the Alexandrov topology induced by R_C and S(P(R_C)) is the family of closed sets of the Alexandrov topology induced by R^⌣_C;”

CEFR level