Unconditionally closed subset

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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