[[Topology MOC]]
# Interior and exterior
The **interior** $\Int (S)$ of a subset $S$ of a [[topological space]] $X$ is the union of all subsets of $S$ that are open in $X$,
i.e. it is the largest open subset of $S$ (which may be $S$ itself). #m/def/topology 
The **exterior** is simply the interior of the compliment $X \setminus S$,
or alternatively it is the compliment of the closure of $S$. #m/def/topology 


## Properties

- The union of the interior with the [[Boundary]] is the [[Closure]] of $S$.

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#state/develop | #lang/en | #SemBr