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Regular Surface

A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V intersection M such that

1. x is differentiable,

2. x:U->V intersection M is a homeomorphism, and

3. Each map x:U->M is a regular patch.

Any open subset of a regular surface is also a regular surface.

See also

Regular Patch

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References

Gray, A. "The Definition of a Regular Surface in R^n." §12.4 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 281-286, 1997.

Referenced on Wolfram|Alpha

Regular Surface

Cite this as:

Weisstein, Eric W. "Regular Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RegularSurface.html

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