The one-point compactification $\mathbb{N}_\infty$ of $\mathbb{N}$ is obtained from the discrete space $\mathbb{N}$ by adjoining a limit point $\infty$. It may be identified with the subspace of Cantor space $$ \mathbb{N}_\infty = \{ \alpha \in \{0,1\}^\mathbb{N} \mid \forall n \,.\, \alpha_n \ge...