Let $(X,\mathscr{T})$ be a Topological Space. $X$ is a Hausdorff space if for each distinct $x_{1},x_{2}\in X$ (i.e., $x_{1}\neq x_{2}$), there exists neighbourhoods $\mathcal{U}_{1}$ of $x_{1}$ and $\mathcal{U}_{2}$ of $x_{2}$ such that $$\mathcal{U}_{1}\cap \mathcal{U}_{2}=\emptyset.$$ i.e. for any two points we can find some “space” between these points to “house” them off from each other.