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Limit (in a Topological Space)**

Given a topological space \((X,\mathcal{T})\) and a sequence \((a_i)_{i=1}^n\) in \(X\), a point \(L\in X\) is a limit of the sequence if, for any open neighbourhood of \(L\), there is a point in the sequence beyond which all terms lie within that neighbourhood: \(\forall U\in\mathcal{T}:L\in U\Rightarrow( \exists N>0:\forall n>N:a_n\in U)\). In a general topological space, the limit is not necessarily unique.