Definition:Ball/Also known as
Ball: Also known as
Instead of ball, some sources use the term disk (or disc] in British English).
Some sources use disk (or disc) specifically to mean closed ball, and use open disk (or open disc) for open ball.
$\mathsf{Pr} \infty \mathsf{fWiki}$ prefers to reserve the term disk, if at all, for a disk in the complex plane, as there is an intuitive $2$-dimensional nuance to the word disk, while ball guides intuition down the path of $3$ dimensions.
The Concise Oxford Dictionary of Mathematics distinguishes between a disc, which is what it is in its context of a circle in the plane, and a disk, which is used as a synonym for an open or closed ball in a general metric space.
However, this is not how we roll at $\mathsf{Pr} \infty \mathsf{fWiki}$, where the aim is that open ball and closed ball are to be used consistently.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): disk or disc
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): disc (disk)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): disc (disk)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): disk