Discontinuous group

A discontinuous group is a mathematical concept relating to mappings in topological space.
Definition.
Let formula_1 be a topological space of points formula_2, and let formula_3, formula_4, be an open continuous representation of the topological group formula_5 as a transitive group of homeomorphic mappings of formula_1 on itself. The representation formula_7 formula_8 of the discrete subgroup formula_9 in formula_1 is called discontinuous, if no sequence formula_11 (formula_12) converges to a point in formula_1, as formula_14 runs over distinct elements of formula_15.