In mathematics, a paratopological group is a topological semigroup that is algebraically a group. 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.
Compact paratopological groups are automatically topological groups.
References
- Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.
- A. V. Arhangelskii. Topological spaces connected to algebraic structures Archived 2011-06-08 at the Wayback Machine
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