Neighbourhood | Neighborhood (English)
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Definition (undergraduate level)
In a metric space, the ε neighbourhood of a point P is the set of all points whose distance from P is less than ε.
In a topological space X, a neighbourhood of a point p is any subset of X which contains an open set which contains p.
In a topological space X, a neighbourhood of a point p is any subset of X which contains an open set which contains p.
Definition (undergraduate level)
The subset W of topological space X is a neighbourhood of x ∈ X if there is an open subset U of W with x ∈ U .
Relations
- broader:
- (en) Set
- references:
- (en) Metric space
- (en) Topological space
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