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from wikipedia: "Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface"

Now, hyper- is the prefix of "over" hypo- is the prefix of "under"

If we move form n to n-1 soundn't it be called Hyposurface?

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    @Vhailor- Publish your comment as a question and I will select it2011-05-03

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The "hyper" prefix is used since hypersurfaces are the higher-dimensional analogs of regular two-dimensional surfaces.

It is used in the same way in expressions such as "hyperplane" and "hypercube".