Unconditionally closed subset
This article defines a property of subsets of groups
View other properties of subsets of groups|View properties of subsets of abelian groups|View subgroup properties
Definition
A subset of a group is termed an unconditionally closed subset of if is a closed subset of for any topology on that turns into a T0 topological group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| elementary algebraic subset | |FULL LIST, MORE INFO | |||
| algebraic subset | |FULL LIST, MORE INFO |