Alexandroff space

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This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces


A topological space is termed a principal space or Alexandroff space if it satisfies the following equivalent conditions:

  • Every point has a unique minimal neighbourhood
  • An arbitrary union of open subsets is open
  • An arbitrary union of closed subsets is closed

Relation with other properties

Stronger properties

Weaker properties