Definition:Neighborhood (Neighborhood Space)
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Definition
Let $\struct {S, \NN}$ be a neighborhood space.
Let $x \in S$.
Let $\NN_x$ satisfy the neighborhood space axioms.
Then each element $N$ of $\NN_x$ is called a neighborhood of $x$.
Also see
- Results about neighborhoods can be found here.
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 3$: Neighborhoods and Neighborhood Spaces: Definition $3.4$