# Interior

From Topospaces

## Definition

Suppose is a topological space and is a subset of . The **interior** of in is defined in the following equivalent ways:

- It is the unique
*largest*open subset of that is contained in . - It is the union of all open subsets of contained in .
- It is the set of all points for which there exists an open subset that is completely contained in .
- It is the set-theoretic complement in of the closure of the complement of in .

## Related notions

- Open subset: A subset is open iff it equals its own interior.
- Regular open subset: A subset is regular open iff it equals the interior of its closure.