Locally compact abelian group

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This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)
View a complete list of such properties

Definition

A locally compact abelian group (also called a LCA group) is a topological group that is a locally compact group (i.e., its underlying topological space is a locally compact space) as well as an abelian group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
discrete abelian group
compact abelian group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian topological group
unimodular group locally compact group that admits a bi-invariant Haar measure
locally compact group