Door space

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In topology, a door space is a topological space in which each subset is open or closed or both.


  • A discrete space is a door space since each subset is both open and closed.
  • The subset of the real numbers with the usual topology is a door space. Any set containing the point 0 is closed: any set not containing the point 0 is open.


  • J.L. Kelley (1955). General topology. van Nostrand, 76.