Disk (mathematics)

In geometry, a disk (also spelled disc)^[1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.^[2]

For a radius ${\displaystyle r}$, an open disk is usually denoted as ${\displaystyle D_{r}}$, and a closed disk is ${\displaystyle {\overline {D_{r}}}}$. However in the field of topology the closed disk is usually denoted as ${\displaystyle D^{2}}$, while the open disk is ${\displaystyle \operatorname {int} D^{2}}$.