Kleinian group

Definition
The term Kleinian group is used for any closed subgroup of projective special linear group:PSL(2,C) (the projective special linear group of degree two $$PSL(2,\mathbb{C})$$ over the field of complex numbers) that is discrete in the subspace topology. Note that we are using the natural topology on $$PSL(2,\mathbb{C})$$ arising as a quotient topology from $$SL(2,\mathbb{C})$$, which in turn acquires a subspace topology from the space of $$2 \times 2$$ matrices over $$\mathbb{C}$$, which in turn is identified with $$\mathbb{C}^4 \cong \mathbb{R}^8$$.