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Neighbourhood system

In topology and related areas of mathematics, the neighbourhood system, complete system of neighbourhoods, or neighbourhood filter N ( x ) {\displaystyle {\mathcal {N}}(x)} for a point x {\displaystyle x} in a topological space is the collection of all neighbourhoods of x . {\displaystyle x.}

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Neighbourhood system

Nodes56
Edges55
Triples0
Avg. degree1.96
Density0.035714
Components1

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Important terminology

displaystyle neighbourhood topology mathcal point basis space topological set filter open subseteq subset neighbourhoods system neighborhood contains every left right

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