I'm having trouble with a concept about piecewise linear paths. I've been looking on the net but I haven't found a definition of it.
Consider a finite family of hyperplanes in a finite-dimension real vector space $V$. What does it mean that a piecewise-linear path in $V$ is in general position with respect to the family of hyperplanes? And how do you prove that a piecewise-linear or smooth path can be approximated by one in general position?