\begin{definition}[Definition:Locally Euclidean Space]
Let $M$ be a topological space.
Let $d \in \N$ be a natural number.
Then $M$ is a '''locally Euclidean space''' of dimension $d$ if each point in $M$ has an open neighbourhood which is homeomorphic to an open subset of Euclidean space $\R^d$.
\end{definition}