Bounded function

Set

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$

Discussion

For linear operators between normed vector spaces, being bounded for each input element and continuous coincide.

Reference

Wikipedia: Bounded function

Parents

Subset of

Function

Context

Metric