Editing Bounded function (section)

== Related notions ==
Weaker than boundedness is [[local boundedness]]. A family of bounded functions may be [[Uniform boundedness|uniformly bounded]]. 

A [[bounded operator]] ''<math>T: X \rightarrow Y</math>'' is not a bounded function in the sense of this page's definition (unless <math>T=0</math>), but has the weaker property of '''preserving boundedness'''; bounded sets <math>M \subseteq X</math> are mapped to bounded sets ''<math>T(M) \subseteq Y</math>.'' This definition can be extended to any function <math>f: X \rightarrow Y</math> if ''<math>X</math>'' and ''<math>Y</math>'' allow for the concept of a bounded set. Boundedness can also be determined by looking at a graph.{{Citation needed|date= September 2021}}