Definition:Basis for Open Sets (Metric Space)

Definition

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

Let $\BB$ be a set of open sets of $M$.

Then $\BB$ is a basis for the open sets of $M$ if and only if:

for each open set $U$ of $M$, $U$ is the union of sets of $\BB$.

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 6$: Open Sets and Closed Sets: Exercise $1$