Definition of topological manifolds with dimension zero/locally euclidean of dimension zero

Question

A topological $n$-manifold $M$ is locally Euclidean of dimension $n$ (each point of $M$ has a neighborhood that is homeomorphic to an open subset of $\mathbb{R}^n)$.

But what does locally Euclidean of dimension 0 mean?

Answer 1

$\Bbb R^0$ is just a point, isn't it? Hence locally Euclidean of dimension zero means that locally homeomorphic to $\Bbb R^0=\{pt\}$. A $0-$topological manifold is then a countable set endowed with the discrete topology.