Submaximal space

Definition
A topological space is termed submaximal if it satisfies the following equivalent conditions:


 * 1) Every subset of it is locally closed, i.e., an intersection of an defining ingredient::open subset and a defining ingredient::closed subset.
 * 2) Every defining ingredient::dense subset is open.
 * 3) Every defining ingredient::preopen subset is open.

Stronger properties

 * Door space

Weaker properties

 * Weakly submaximal space