Editing Smoothness (section)

===Smooth functions between subsets of manifolds===

There is a corresponding notion of '''smooth map''' for arbitrary subsets of manifolds.  If <math>f : X \to Y</math> is a [[Function (mathematics)|function]] whose [[Domain of a function|domain]] and [[Range of a function|range]] are subsets of manifolds <math>X \subseteq M</math> and <math>Y \subseteq N</math> respectively. <math>f</math> is said to be '''smooth''' if for all <math>x \in X</math> there is an open set <math>U \subseteq M</math> with <math>x \in U</math> and a smooth function <math>F : U \to N</math> such that <math>F(p) = f(p)</math> for all <math>p \in U \cap X.</math>