In
mathematics, a paratopological group is a
topological semigroup that is algebraically a
group
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic ide ...
. 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 mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two st ...
in that the group inverse is not required to be continuous.
As with topological groups, some authors require the topology to be
Hausdorff.
[A. V. Arhangelskii]
Topological spaces connected to algebraic structures
Compact paratopological groups are automatically topological groups.
References
Topological groups
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