properly discontinuous action造句

• For a properly discontinuous action, cocompactness is equivalent to compactness of the quotient space " X / G ".
• Generalising the example of the modular group a Fuchsian group is a group admitting a properly discontinuous action on the hyperbolic plane ( equivalently, a discrete subgroup of \ mathrm { SL } _ 2 ( \ mathbb R ) ).
• Every free, properly discontinuous action of a group " G " on a path-connected topological space " X " arises in this manner : the quotient map is a regular covering map, and the deck transformation group is the given action of " G " on " X ".
• Relatively hyperbolic groups are a class generalising hyperbolic groups . " Very " roughly G is hyperbolic relative to a collection \ mathcal G of subgroups if it admits a ( " not necessarily cocompact " ) properly discontinuous action on a proper hyperbolic space X which is " nice " on the boundary of X and such that the stabilisers in G of points on the boundary are subgroups in \ mathcal G.