Definition:Neighborhood (Metric Space)/Compact Subset
< Definition:Neighborhood (Metric Space)(Redirected from Definition:Neighborhood of Compact Subset of Metric Space)
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This page is about neighborhood in the context of metric spaces. For other uses, see neighborhood.
Definition
Let $M = \struct {A, d}$ be a metric space.
Let $K \subseteq A$ be a compact subset of $A$.
The $\epsilon$-neighborhood of $K$ in $M$ defined and denoted as:
- $\map {\NN_\epsilon} K := \set {x \in A: \exists y \in K: \map d {x, y} \le \epsilon}$
Also see
- Results about neighborhoods can be found here.
Linguistic Note
The UK English spelling of neighborhood is neighbourhood.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hausdorff metric