piecewise smooth
A curve $\alpha :[a,b]\to {\mathbb{R}}^{n}$ is said to be piecewise smooth if each component ${\alpha}_{1},\mathrm{\dots},{\alpha}_{n}$ of $\alpha $ has a bounded derivative ${\alpha}_{i}^{\prime}\mathit{\hspace{1em}}(i=1,\mathrm{\dots},n)$ which is continuous^{} everywhere in $[a,b]$ except (possibly) at a finite number of points at which left and rightsided derivatives exist.

•
Every piecewise smooth curve is rectifiable.

•
Every rectifiable curve can be approximated by piecewise smooth curves.
Title  piecewise smooth 

Canonical name  PiecewiseSmooth 
Date of creation  20130322 12:53:26 
Last modified on  20130322 12:53:26 
Owner  cvalente (11260) 
Last modified by  cvalente (11260) 
Numerical id  7 
Author  cvalente (11260) 
Entry type  Definition 
Classification  msc 51N05 
Related topic  Rectifiable 