Category:Definitions/Bounded Below Mappings

This category contains definitions related to Bounded Below Mappings.
Related results can be found in Category:Bounded Below Mappings.

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

Then $f$ is said to be bounded below (in $T$) by the lower bound $L$ if and only if:

$\forall x \in S: L \preceq \map f x$

That is, iff $f \sqbrk S = \set {\map f x: x \in S}$ is bounded below by $L$.