Regular open subset

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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