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High Quality Content by WIKIPEDIA articles! In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology. Topological groups allow one to study the notion of continuous symmetries in the form of continuous group actions. Although we do not do so here, many authors require that the topology on G be Hausdorff. The reasons, and some equivalent conditions, are discussed below. In the end, this is not a serious restriction-any topological group can be made Hausdorff in a canonical fashion.