===== Bounded function =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ \langle X,d\rangle $ ... metric space |

| @#FFBB00: definiendum | @#FFBB00: $f\in \text{BoundedFunction}(X)$ |

| @#DDDDDD: range       | @#DDDDDD: $x,a\in X$ |
| @#DDDDDD: range       | @#DDDDDD: $M\in \mathbb R$ |

| @#55EE55: postulate   | @#55EE55: $ \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: [[http://en.wikipedia.org/wiki/Bounded_function|Bounded function]]
==== Parents ====
=== Subset of ===
[[Function]]
=== Context ===
[[Metric]]