Submaximal space

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In mathematics, in the realm of topology, a topological space is said to be submaximal if every subset of it is locally closed, that is, every subset is the intersection of an open set and a closed set.

Here are some facts about submaximality as a property of topological spaces:

  • Every door space is submaximal.
  • Every submaximal space is weakly submaximal viz every finite set is locally closed.

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