Discontinuous group

A discontinuous group is a mathematical concept relating to mappings in topological space.

Definition

Let $T$ be a topological space of points $τ$ , and let $τ \to f (τ, x)$ , $x \in G$ , be an open continuous representation of the topological group $G$ as a transitive group of homeomorphic mappings of $T$ on itself. The representation $τ \to f (τ, a)$ $a \in H$ of the discrete subgroup $H \subset G$ in $T$ is called discontinuous, if no sequence $f (τ, a_{n})$ ( $n = 1, 2, \dots$ ) converges to a point in $T$ , as $a_{n}$ runs over distinct elements of $H$ .^[1]

References

↑ Carl Ludwig Siegel (1943), Annals of Mathematics (ed.), Discontinuous groups, vol. 44, pp. 674−689

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[1] Carl Ludwig Siegel (1943), Annals of Mathematics (ed.), Discontinuous groups, vol. 44, pp. 674−689

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