# Definition:Locally Euclidean Space

## Definition

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 homeomorphic to an open subset of Euclidean space $\R^d$.

### Complex Locally Euclidean Space

$M$ is a complex locally Euclidean space of dimension $d$ if and only if each point in $M$ has an open neighbourhood homeomorphic to an open subset of complex Euclidean space $\C^d$.