Discrete group
From Groupprops
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
Contents
Definition
A discrete group is a topological group whose underlying topological space is a discrete space.
Every abstract group can be uniquely given the structure of a discrete group. For a finite group, a discrete group structure is the only way of giving it the structure of a T0 topological group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Amenable discrete group |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Locally compact group |
