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The set of all points $x$ of a subset $A$ of a topological space $X$ for which an open set $U_x$ in $X$ exists such that $x \in U \subset A$. The interior of the set $A$ is usually denoted by $\mathrm{Int}\, A $ and represents the largest open set in $X$ contained in $A$. The equality $\mathrm{Int}\, A = X \setminus [X \setminus A]$ holds, where $[]$ denotes closure in $X$.  The interior is sometimes called the ''open kernel'' of the set.

The interior of a closed set in a topological space $X$ is a regular open or [[canonical set]]. Spaces in which the open canonical sets form a [[base]] for the topology are called semi-regular. Every regular space is semi-regular. 

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See also [[Interior of a set]].