# Regular open subset

From Topospaces

*This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces*

## Definition

A subset of a topological space is termed a **regular open subset** if it satisfies the following equivalent conditions:

- It equals the interior of its closure.
- It occurs as the interior of a closed subset.

## Relation with other properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

open subset |