Semiopen 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 semiopen subset if it is contained in the closure of its interior.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
open subset	equals its own interior
regular open subset	equals the interior of its closure
alpha-set	contained in the interior of the closure of its interior