Locally compact abelian group
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 |