A continuous group is a group equipped with a topology in which the group operation and the map taking each group element to its inverse element are continuous. With the additional requirement of a T2-space, this is a topological group.
These continuity conditions do not require a group to be infinite. Every group, including a finite group, satisfies these requirements when equipped with the discrete topology. The integers under addition with the discrete topology and the rational numbers under addition with the topology inherited from the real line also satisfy the continuity requirement. By comparison, a Lie group of positive dimension is necessarily infinite.
