Properly Discontinuous Action

Properly Discontinuous Action

In topology and related branches of mathematics, an action of a group G on a topological space X is called proper if the map from G×X to X×X taking (g,x) to (gx,x) is proper, and is called properly discontinuous if in addition G is discrete. There are several other similar but inequivalent properties of group actions that are often confused with properly discontinuous actions.

Read more about Properly Discontinuous Action:  Properly Discontinuous Action, Similar Properties

Famous quotes containing the words properly and/or action:

    For the “superior morality” of which we hear so much, we too would desire to be thankful: at the same time, it were but blindness to deny that this “superior morality” is properly rather an “inferior criminality” produced not by greater love of Virtue, but by greater perfection of Police; and of that far subtler and stronger Police, called Public Opinion.
    Thomas Carlyle (1795–1881)

    For the child whose impulsiveness is indulged, who retains his primitive-discharge mechanisms, is not only an ill-behaved child but a child whose intellectual development is slowed down. No matter how well he is endowed intellectually, if direct action and immediate gratification are the guiding principles of his behavior, there will be less incentive to develop the higher mental processes, to reason, to employ the imagination creatively. . . .
    Selma H. Fraiberg (20th century)