A disc of unit radius on a plane is called a unit disc. Unless otherwise specified, the unit disc on a Cartesian plane is the unit disc about the origin. The unit disc may be either closed or open, that is to say, either be

closed: the set of points with radius less than or equal to one from the centre
open: the set of points with radius less than one from the centre

See also: open interval, closed interval, open set, closed set