door

Definition

A topological space (X,τ) is said to be door if each subset of X is either open or closed.

Property

• door ⇒ submaximal
• door ⇒ T_{EF}. [2]

Reference

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