Hausdorff Space
Definition
A topological space \(X\) is said to be a Hausdorff space if for every \(x, y \in X\) with \(x \neq y\), there exists neighbourhoods \(G_{x}\) around \(x\) and \(G_{y}\) around \(y\) such that \(G_{x} \cap G_{y} \neq \varnothing\).
This is one of the separation axioms, and is particularly useful in that it is a sufficient condition for uniqueness of limits of sequences and an equivalent condition for uniqueness of limits of nets.