## Regular Surface

A Subset is called a regular surface if for each point , there exists a Neighborhood of in and a Map of an Open Set onto such that

1. is differentiable,

2. is a Homeomorphism, and

3. Each map is a Regular Patch.
Any open subset of a regular surface is also a regular surface.

References

Gray, A. The Definition of a Regular Surface in .'' §10.4 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 195-200, 1993.