# Is any continuous curve in $\mathbb{R}^n$ a 1-D manifold?

I wonder if there is any theorem stating that any continuous curve in $\mathbb{R}^n$ is a 1-D manifold.

If not, can anyone provide an example?

At first I thought maybe a Peano curve affords a counterexample, but it seems not...

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What is your definition of a manifold? And think about the curve having self-intersection. –  ronno Oct 29 '12 at 14:03