Alexandrov topology

English

Etymology

Along with the closely related concept of Template:M, after Russian mathematician Template:W.

Noun

1. Template:Lb A topology in which the intersection of any family of open sets is an open set.
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   • Template:Quote-book
   • 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, Template:W 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 $R_C^{⌣}$;

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.