*Definition [#d4b44465]
A topological space (X,τ) is said to be door if each subset of X is either open or closed.

*Property [#u4717f70]
-door ⇒ [[submaximal]]
-door ⇒ [[T_{EF}]]. [2]

*Reference [#a93733b5]
+Kennedy, G. J.; McCartan, S. D., ''Minimal weakly submaximal topologies.'' (English summary), Math. Proc. R. Ir. Acad. 99A (1999), no. 2, 133–140. 
+McSherry, D. M. G. , ''On separation axioms weaker than T_1.'' , Proc. Roy. Irish Acad. Sect. A 74 (1974), 115–118.