Is $(\mathbb{Z},\mathcal{P}(\mathbb{Z}))$ a manifold?

Question

Consider the topological space $(\mathbb{Z},\mathcal{P}(\mathbb{Z}))$. It is clearly Hausdorff since $(\mathbb{Z},\mathcal{P}(\mathbb{Z}))$ can be seen as a metric space where the topology is induced by the discrete metric. Furthermore, it is clearly second-countable since a countable basis is given by $$\{\{n\} : n \in \mathbb{Z}\}$$ Now my question is, is this space also a manifold and of which dimension? I would say, that it is a $0$-dimensional manifold since if $x \in \mathbb{Z}$, $\{x\}$ is a neighbourhood of $x$ and clearly homeomorphic to the one-point set $\mathbb{R}^0$. Is that correct?