Paratopological group

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.

References

1. Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.
2. A. V. Arhangelskii. Topological spaces connected to algebraic structures