Definition:Bounded

Ordered Set
Let $$\left({S; \le}\right)$$ be a poset.

Let $$T \subseteq S$$ be both bounded below and bounded above in $$S$$.

Then $$T$$ is bounded in $$S$$.

Mapping
Let $$\left({T; \le}\right)$$ be a poset.

Let $$f: S \to T$$ be a mapping.

Let the range of $$f$$ be bounded.

Then $$f$$ is defined as being bounded.