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What does it mean to say that a curve in $\mathbb{R}^2$ is embedded? I think a curve in $\mathbb{R}^3$ is embedded if it lies on a plane, but what does it mean in 2d? I searched everywhere but I can't find an answer.

Also, is there a simple way of seeing an immersive curve in $\mathbb{R}^2$?

Thanks

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    The difference between an immersion and an embedding is that the former does not need to be injective. See http://en.wikipedia.org/wiki/Immersion_%28mathematics%292012-06-26
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    Also, even when an immersion is injective, it need not be a homeomorphism onto its image.2012-06-26
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    And a curve embedded into $\mathbb{R}^3$ need not lie on a plane - for example, a helix.2012-06-26

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