Regular open subset

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:

1. It equals the interior of its closure.
2. 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