What is the best way to intuitively and visually distinguish between immersion and submersions? For example, I understand that the standard picture of the Klein Bottle in R^3 is an immersion. How do I see this? (Obviously, it's not an embedding because the Klein Bottle self-intersects in R^3. But how do I see that the differential map is 1-to-1 but not onto?) What would a submersion look like?(adsbygoogle = window.adsbygoogle || []).push({});

Also, can I visualize a copy of the real line in R^3 so that, it is an immersion but not a submersion nor an embedding? Also as a submersion but not an immersion?

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# Visualizing Immersions vs. Submersions

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