Discontinuous group explained

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

Definition

Let

T be a topological space of points \tau , and let \tau\to f(\tau,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 \tau\to f(\tau,a) a\in H of the discrete subgroup H\sub G in T is called discontinuous, if no sequence f(\tau,a _{n)} (n =1 , 2 ,\ldots ) converges to a point in T , as a _{n} runs over distinct elements of H