 In two dimensions, closed disks are compact since for any infinite number of points sampled from a disk, some subset of those points must get arbitrarily close either to a point within the disc, or to a point on the boundary.However, an open disk is not compact, because a sequence of points can tend to the boundary—without getting arbitrarily close to any point in the interior.Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can still tend to the missing point, thereby not getting arbitrarily close to any point "within" the space.