Paratopological group

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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.