Paratopological group

In mathematics, a paratopological group is a topological semigroup "G" which is algebraically a group. [Artur Hideyuki Tomita. [http://tatra.mat.savba.sk/Full/14/10tomita.ps On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.] ] Thus, the group's product operation must be a continuous function from "G" × "G" to "G", but the group inverse need not be continuous. A topological group by comparison, must have a continuous inverse.

Another definition [A. V. Arhangelskii. [http://atlas-conferences.com/c/a/v/h/18.htm Topological spaces connected to algebraic structures] ] is that a "paratopological group" is a group with a Hausdorff topology such that the group operation is jointly continuous.

References