# Interior (topology)

## Largest open subset of some given set / From Wikipedia, the free encyclopedia

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In mathematics, specifically in topology,
the **interior** of a subset S of a topological space X is the union of all subsets of S that are open in X.
A point that is in the interior of S is an **interior point** of S.

Largest open subset of some given set

The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

The **exterior** of a set S is the complement of the closure of S; it consists of the points that are in neither the set nor its boundary.
The interior, boundary, and exterior of a subset together partition the whole space into three blocks (or fewer when one or more of these is empty).