Definition:Region/Metric Space
Jump to navigation
Jump to search
Definition
Let $M = \struct {A, d}$ be a metric space.
A region of $M$ is a subset $U$ of $M$ such that $U$ is:
- $(1): \quad$ non-empty
- $(2): \quad$ path-connected.
Also defined as
Some sources insist that in order for a subset of a metric space to be a region it must also be open.