##  [Alexandrov Topology](/index.php/alexandrov-topology) 

  ##  [Alexandrov Topology](https://puremath.quantumdictionary.io/alexandrov-topology-0) 

  

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Definition

A topology in which arbitrary intersections of open sets are open (equivalently every point has a smallest neighborhood); such topologies correspond exactly to preorders on the underlying set via the specialization order, and are often called Alexandrov (or Alexandroff) topologies.