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Neighbourhood**

Given a toplogical space \((X,\mathcal{T})\), a neighbourhood of a point \(x\in X\) is a subset \(A\subseteq X\) which contains an open set containing \(x\); \(exists U\in \mathcal{T}:x\in U\subseteq A\). Often when one talks of a neighbourhood of \(x\), they just mean an open set containing \(x\).