Discrete 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 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