Interior of a set

$X$ in a topological space $Y$

The set of interior points of $X$ (cf. Interior point of a set). It is usually denoted by $\operatorname{Int}X$. Invariably, $\operatorname{Int}X=X\setminus[Y\setminus X]=X\setminus\operatorname{Fr}x$, where $\operatorname{Fr}$ is the boundary of $X$. The interior of $X$ is also equal to the union of all subsets of $X$ that are open in the entire space. The interior of a set is sometimes known as the open kernel.