In mathematics, a paratopological group is a topological semigroup that is algebraically a group.[1] In other words, it is a group G with a topology such that the group's product operation is a continuous function from G × G to G. This differs from the definition of a topological group in that the group inverse is not required to be continuous.
As with topological groups, some authors require the topology to be Hausdorff.[2]
Compact paratopological groups are automatically topological groups.