Category:Definitions/Local Boundedness

This category contains definitions related to Local Boundedness.
Related results can be found in Category:Local Boundedness.

Let $M = \struct {A, d}$ be a metric space.

Let $f$ be a mapping defined on $M$.

Then $f$ is said to be locally bounded if and only if:

for all $x \in A$, there is some neighbourhood $N$ of $x$ such that $f \sqbrk N$ is bounded.