Paratopological group
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In mathematics, a paratopological group is a topological semigroup G which is algebraically a group.[1] 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[2] is that a paratopological group is a group with a Hausdorff topology such that the group operation is jointly continuous.
[edit] 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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