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 $S$ of a group $G$ is termed an unconditionally closed subset of $G$ if $S$ is a closed subset of $G$ for any topology on $G$ that turns $G$ 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