Definition:Topological Group

Definition
Let $\struct {G, \odot}$ be a group.

On its underlying set $G$, let $\struct {G, \tau}$ be a topological space.

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

Also see

 * Equivalence of Definitions of Topological Group


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