Unconditionally closed subgroup

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A subgroup $H$ of a group $G$ is termed an unconditionally closed subgroup if $H$ is a closed subgroup of $G$ for any topology on $G$ that turns $G$ into a T0 topological group.

Relation with other properties

Corresponding subset property

• Unconditionally closed subset is the "subset" version of the property.

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite subgroup				|FULL LIST, MORE INFO
c-closed subgroup				|FULL LIST, MORE INFO
algebraic subgroup				|FULL LIST, MORE INFO
marginal subgroup				|FULL LIST, MORE INFO
weakly marginal subgroup				|FULL LIST, MORE INFO