Let $\tau = \{U\subseteq \mathbb{N} : \mathbb{N} - U$ is finite $\}\cup \{\emptyset\}$. This defines a topology on $\mathbb{N}$.

Is $(\mathbb{N},\tau)$ a Hausdorff space?

If not, give all valid reasons why this space cannot be a Hausdorff space.

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