# Definition:Open Ball/Also known as

## Terminology for Open Ball

There are various names and notations that can be found in the literature for this concept, for example:

**Open $\epsilon$-ball neighborhood of $a$**(and in deference to the word**neighborhood**the notation $N_\epsilon \left({a}\right)$, $N \left({a, \epsilon}\right)$ or $N \left({a; \epsilon}\right)$ are often seen)**Spherical neighborhood of $a$****Open sphere at $a$****Open $\epsilon$-ball centered at $a$****$\epsilon$-ball at $a$**.

The notation $B \left({a; \epsilon}\right)$ can be found for $B_\epsilon \left({a}\right)$, particularly when $\epsilon$ is a more complicated expression than a constant.

Similarly, some sources allow $B_d \left({a; \epsilon}\right)$ to be used for $B_\epsilon \left({a; d}\right)$.

It needs to be noticed that the two styles of notation allow a potential source of confusion, so it is important to be certain which one is meant.

Rather than say **epsilon-ball**, as would be technically correct, the savvy modern mathematician will voice this as the conveniently bisyllabic **e-ball**, to the apoplexy of his professor. And at least one contributor to this site does not believe that nobody actually says **open epsilon-ball neighborhood** very often, whatever opportunities to do so may arise. Life is just too short.

The term **neighborhood** is usually used nowadays for a concept more general than an **open ball**: see Neighborhood (Metric Space).