Definition:Bounded Above Mapping/Unbounded

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This page is about Unbounded Above in the context of Mapping. For other uses, see Unbounded Above.


Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.

Then $f$ is unbounded above on $S$ if and only if it is not bounded above on $S$:

$\neg \exists H \in T: \forall x \in S: \map f x \preceq H$

Also see

  • Results about unbounded above mappings can be found here.