continuity and open subset

let say E is a subset of R and f be the real number function o E then f is continuou on E if an only if $f^{-1}(V)$ is open in E for every open subset $V$ of $R$

what is opn subset V mean? in a continuous function?I thought open set mean the set contain all its interier pointsbut what open set mean in he conticuose function

and also what is the closed set mean in continuous function?