Topological Groups and Semigroups
Yurii Il'ich Lyubich · Birkhäuser Basel eBooks · 1988
1°. A topological group is a group endowed with a Hausdorff topology relative to which the operations of multiplication and inversion are continuous (the latter being therefore a homeomorphism); here the Cartesian product of the group with itself is endowed with the product topology. [The Hausdorff requirement is not included by all authors in the definition of a topological group. It can be in fact relaxed, without restricting the class of groups, to axiom T 0 : for any two distinct points there is a neighborhood of one of them that does not contain the other.] These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.