Definition:Locally Euclidean Space

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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 $\C^d$.


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