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
edit- ^ 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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