elements of topology is open set? Let's consider the topological space $(\mathbb{R},2^\mathbb{R})$, then each interval is element of topology $2^\mathbb{R}$, but as usually, we consider $[a,b]$ as as closed set.
So my question is 


*

*Is $[a,b]$ an open set in topology $2^\mathbb{R}$

*Does the definition of open set come after the specific topology?


Every set including closed intervals is open in that topology: that's what $2^{\mathbb R}$ means: It contains every set.
Every set is also closed in that topology, since a closed set in a topological space is simply any set whose complement is open.
The topology is simply the collection of all open sets in the space.
