| context | $ \langle X,d\rangle $ … metric space |
| definiendum | $f\in \text{BoundedFunction}(X)$ |
| range | $x,a\in X$ |
| range | $M\in \mathbb R$ |
| postulate | $ \exists a, M.\ \forall x.\ d(f(x),a) < M$ |
For linear operators between normed vector spaces, being bounded for each input element and continuous coincide.
Wikipedia: Bounded function