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Properly DiscontinuousIn topology and related branches of mathematics, an action of a group G on a topological space X is called properly discontinuous if every element of X has a neighborhood that moves outside itself under the action of any group element but the trivial element. The action of the deck transformation group of a cover is an example of such action. The formal definition is as follows. Let a group G act on a topological space X by homeomorphisms. This action is called properly discontinuous if, for every x in X, there is a neighborhood U of x such that -
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