Paratopological group
From HandWiki
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
- ↑ Artur Hideyuki Tomita. On sequentially compact both-sides cancellative semigroups with sequentially continuous addition.
- ↑ A. V. Arhangelskii. Topological spaces connected to algebraic structures
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