Kleinian group

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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.