Definition:Euclidean Space/Riemannian Manifold

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Definition

Let $\struct {M, g}$ be a Riemannian manifold where $M = \R^n$ for some $n \in \N_{> 0}$ and $g$ is the Euclidean metric.


Then $\struct {M, g}$ is known as the ($n$-dimensional) Euclidean space.


Sources