Discrete groups and discontinuous actions (Q1382727)

In the many contexts in which quotient spaces arise by group actions, the most convenient notion of ``discontinuous action'' is chosen to suit the context. As a result, there is a lack of agreement and sometimes, clarity, about this notion. This paper discusses the varying definitions in a semi-expository manner, and clarifies the interrelationships between them making use of some neat examples. It highlights the conditions under which a quotient space is Hausdorff and the role of the most appropriate topology in spaces of isometries.