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 |