Definition:Topological Group

Definition
Let $\left({G, \odot}\right)$ be a group.

On its underlying set $G$, let $\left({G, \tau}\right)$ be a topological space.

Equivalence of Definitions
That the definitions presented above are equivalent is shown on Equivalence of Definitions of Topological Group.

Also defined as
Some sources insist that a topological group be a Hausdorff space.

Also see

 * Definition:Topological Ring
 * Definition:Topological Field
 * Definition:Topological Vector Space