Interior of a subset

The interior $\operatorname{int}(A)$ of a subset $A$ of a topological space $X$ is the largest open set contained in $A$.
It can be shown that it is the union of all open sets contained in $A$ :
$$\operatorname{int}(A)=\bigcup\{U \subseteq X: U \text { open, } U \subseteq A\}$$