Definition:System of Neighborhoods
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Definition
Let $M = \struct {A, d}$ be a metric space.
Let $a \in A$.
Let $\NN_a$ be the set of all neighborhoods of $a$ in $M$.
Then $\NN_a$ is the system of neighborhoods of the point $a$.
Also known as
The system of neighborhoods of a point can also be referred to as the complete system of neighborhoods of that point.
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 4$: Open Balls and Neighborhoods: Definition $4.4$