A patch (also called a local surface) is a differentiable mapping 
, where 
is an open subset of 
. More generally, if 
is any subset of 
, then a map 
is a patch provided that 
can be extended to a differentiable map from 
into 
,
where 
is an open set containing 
. Here, 
(or more generally, 
)
is called the map trace of 
.
Patch
See also
Gauss Map, Injective Patch, Map Trace, Monge Patch, Regular PatchExplore with Wolfram|Alpha
References
Gray, A. "Patches in
" and "Patches in 
." §12.1 and 12.2 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 269-278, 1997.Referenced on Wolfram|Alpha
PatchCite this as:
Weisstein, Eric W. "Patch." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Patch.html