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- Thread starter flamengo
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fresh_42

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To answer "Is it closed?" one firstly needs a topology, that defines the terms open and closed. I assume you refer to the standard Euclidean topology here. So you could either consider where the limit points of curves and surfaces have to exists, namely in those curves again, as you cannot find a sequence of points within them, that has a limit outside of them, or, which I think would be easier, consider a point outside, measure its distance to the surface, which is strictly positive, and show that the open ball with radius half this distance and center the point is completely outside the surface, which makes the set outside open and thus the surface closed.

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chiro

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I'd recommend you look at complex analysis [which looks at counting loops if you parameterize them with complex numbers] as well as differential geometry when it comes to curvature.

Some hints when it comes to different kinds of curvature:

https://en.wikipedia.org/wiki/Curvature

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