# Topology with only one open proper set

What is the name of the Topologies that contains only one proper open set? That is if X<>{ } and T={{ }, O,X} ,where O ⊂ X ..I looking for a terminology that represent this topology in general.For me I call them Non-Trivial minimal Topologies .But this is not scientific terminology? please I f there an answer must be supported by a reference ?

• I would rather call it non-trivial open set. – drhab Nov 17 at 14:01
• @drhab I looking for the "official " mathematical terminology for them .If it exist – Taha Topology Nov 17 at 14:11

An infraspace is a topology such that the only topology strictly coarser than it is the trivial topology. Every infraspace topology has on $$E$$ the form $$\{E,A,\emptyset\}$$ where $$A \subset E$$$$A \neq \emptyset$$, $$A \neq E$$.