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Discontinuous group

From Wikipedia, the free encyclopedia

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

Definition

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Let be a topological space of points , and let , , be an open continuous representation of the topological group as a transitive group of homeomorphic mappings of on itself. The representation of the discrete subgroup in is called discontinuous, if no sequence () converges to a point in , as runs over distinct elements of .[1]

References

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